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#Low-Dimensional Topology

Showing: 52 courses
University of Chicago Department of Mathematics

Anosov Flows on 3-Manifolds

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Dive into Anosov flows on 3-manifolds, exploring their chaotic yet stable nature, classification challenges, and recent advancements in low-dimensional geometric topology.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Low-Dimensional Solenoidal Manifolds

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Exploración de manifolds solenoidales de baja dimensión, sus propiedades topológicas y estructurales, y nuevos resultados en este campo de la geometría y topología.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Lecture 4

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Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
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1 Lesons
57 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Using Machine Learning to Formulate Mathematical Conjectures - IPAM at UCLA

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Explore how machine learning aids mathematicians in formulating conjectures, focusing on a discovery linking low-dimensional topology and geometry, with insights on the method's potential and limitations.
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10 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

Square Pegs and Round Holes

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Introduction to lattice homology: algebraic structure for studying three-manifolds. Explores integer lattice approximations of ellipsoids, with implications for navigating institutions not designed for one's needs.
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10 Lesons
25 minutes
On-Demand
Free-Video
IMSA

Subtly Knotted Surfaces Separated by Many Internal Stabilizations

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Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.
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1 Lesons
52 minutes
On-Demand
Free-Video
IMSA

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

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Explore the interaction between hyperbolic geometry and homology cobordism using monopole Floer homology, focusing on subgroups generated by hyperbolic homology spheres.
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1 Lesons
52 minutes
On-Demand
Free-Video
IMSA

Ribbon Concordances and Slice Obstructions: Experiments and Examples

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Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.
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1 Lesons
46 minutes
On-Demand
Free-Video
IMSA

Instantons, Suspension, and Surgery

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Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Instantons, Suspension, and Surgery - Part 1

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Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Fan Ye, Harvard University - 2-Torsions in Singular Instanton Homology

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Exploration of 2-torsions in singular instanton homology for knots, comparing complex and Z/2 coefficients, with focus on fibered knots and genus 1 knot surgeries.
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1 Lesons
1 hour
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Free-Video
IMSA

Instanton Floer Homology and Heegaard Diagrams

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Exploring the connection between instanton Floer homology and Heegaard diagrams in 3-manifolds, with insights on extracting information and potential applications in topology.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces

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Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Fillable Contact Structures From Positive Surgery

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Exploring conditions for fillable contact structures from positive surgery on Legendrian knots, with applications to topological consequences and lens space surgeries.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
IMSA

Rational Slice Genus Bounds from Knot Floer Homology

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Exploring rational slice genus of knots using relative adjunction inequalities and knot Floer homology, with applications to Floer simple knots and insights from 4-dimensional topology.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

PL-Surfaces in Homology 4-Balls

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Exploration of PL-surfaces in homology 4-balls, discussing minimum genus of PL surfaces and their bounds in homology balls using Heegaard Floer homology. Joint research findings presented.
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1 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Equivariant Rokhlin, Eta, and Kappa Invariants of Seifert-Fibered Homology Spheres

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Explore equivariant Rokhlin, eta, and kappa invariants of Seifert-fibered homology spheres in this advanced topology talk, delving into gauge theory applications and low-dimensional manifold properties.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Characterizing Slopes for Alternating Knots

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Exploration des pentes caractérisantes pour les nœuds alternés, examinant leur unicité lors de chirurgies rationnelles et discutant des progrès récents dans ce domaine de la topologie.
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1 Lesons
56 minutes
On-Demand
Free-Video
IMSA

Four-Genus Bounds from the 10/8+4 Theorem

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Explore knot slicing obstructions and four-ball genus bounds using the 10/8+4 theorem. Learn about advanced techniques in gauge theory and low-dimensional topology.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations

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Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
ICTP Mathematics

Measure and Smooth Rigidity of Lattice Actions in Low Dimensions - Federico Rodriguez-Hertz

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Explore measure and smooth rigidity of lattice actions in low dimensions with Federico Rodriguez-Hertz, delving into advanced mathematical concepts and their applications.
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1 Lesons
43 minutes
On-Demand
Free-Video
ICTP Mathematics

Lattices in Low-Dimensional Topology

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Explore advanced concepts in low-dimensional topology, focusing on lattice structures and their applications in geometric and topological analysis.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
ICTP Mathematics

Lattices in Low-Dimensional Topology

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Explore the fascinating intersection of lattice theory and low-dimensional topology, delving into fundamental concepts and their applications in geometric and topological structures.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Mohammed Abouzaid: Bordism and Floer Theory

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Explore the intersection of Morse theory and infinite-dimensional spaces in topology. Learn about recent advances in Floer theory and its applications to generalized homology and derived orbifold bordism.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Heegaard Branes and Exact Results for Non-perturbative Complex Chern-Simons Theory

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Explore Heegaard branes in moduli spaces of Higgs bundles and their applications in mathematics, from geometric Langlands to low-dimensional topology and complex Chern-Simons theory.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Homology Cobordism and the Geometry of Hyperbolic Three-Manifolds

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Explore the interaction between hyperbolic geometry and homology cobordism in low-dimensional topology using monopole Floer homology to study subgroups of the homology cobordism group.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology

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Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Part II

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Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Division, Group Rings, and Negative Curvature in Low-Dimensional Topology

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Explore low-dimensional topology through group rings and division algorithms, focusing on 2-complexes and hyperbolic manifolds. Gain insights into fundamental group structures and cell-decomposition complexity.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

An Approach to Simon's Conjecture

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Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
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1 Lesons
51 minutes
On-Demand
Free-Video
Banach Center

Knots and Categories

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Explore connections between knot theory and category theory, delving into mathematical concepts and their interrelationships in topology and algebra.
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1 Lesons
1 hour 24 minutes
On-Demand
Free-Video
IMSA

Gauge Theory and Low Dimensional Topology - Conference Lecture

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Explore gauge theory and low-dimensional topology with expert insights from Paul Feehan in this engaging 48-minute conference talk at the University of Miami.
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1 Lesons
48 minutes
On-Demand
Free-Video
IMSA

Gauge Theory and Low Dimensional Topology

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Explore gauge theory and low-dimensional topology with insights from MIT expert Tom Mrowka in this conference talk at the University of Miami.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

An Exact Triangle in Monopole Floer Spectra

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Explore an exact triangle for monopole Floer spectra, its application to almost-rational plumbings, and potential future calculations in this advanced topology conference talk.
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1 Lesons
51 minutes
On-Demand
Free-Video
ICTP Mathematics

Lattices in Low-Dimensional Topology

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Explore advanced concepts in low-dimensional topology, focusing on lattice structures and their applications in geometric and topological analysis.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.
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21 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.
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16 Lesons
1 hour 1 minute
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Explore thin position theory for knots, links, and graphs, and its applications to width, tunnel number, and bridge number in topology. Learn about "cut"-incompressible surfaces and additivity of knot invariants.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Explore Morse normal form for branched surfaces and its application in constructing taut foliations, building on Charles Delman's work. Gain insights into advanced topics in low-dimensional topology.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology & Circle-valued Morse Functions

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Explore tangle decompositions in knot theory, focusing on Khovanov homology and immersed curves. Learn how these concepts aid in investigating cosmetic surgery and crossing conjectures.
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1 Lesons
57 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore representations in Homeo_+(S^1) and their role in verifying left-orderability of 3-manifold groups, with applications to the L-space conjecture and taut foliations in various topological settings.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore the Margulis constant in hyperbolic geometry, its significance, and ongoing research to determine its precise value through computational methods and theoretical analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Exploración de límites en el número de asas de variedades suturadas, utilizando argumentos geométricos y desarrollando una función de número de asas en homología de segundo grado.
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1 Lesons
55 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology - Flipping Heegaard Splittings

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Explore Heegaard splittings in topology, focusing on oriented isotopy of splitting surfaces and the possibility of "flipping" sides. Examine contexts, examples, and implications in this advanced mathematical discussion.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore applications of guts in 3-manifolds, including minimal volumes of hyperbolic manifolds and Euler characteristic control in Dehn fillings. Gain insights into advanced topological concepts and their implications.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Explore knot complements, Seifert surfaces, and sutured manifolds in low-dimensional topology. Discover unique decompositions and their implications for the Kakimizu complex and Thurston norm.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore annular links, double branched covers, and annular Khovanov homology. Discover how these concepts relate to braid closures and the wrapping conjecture in low-dimensional topology.
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1 Lesons
57 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore forbidden minor multibranched surfaces and critical complexes in 3-sphere embeddings. Analyze K5 × S1 and K3,3 × S1 families, critical complexes, and their properties in low-dimensional topology.
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1 Lesons
59 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explores non almost-fibered knots in 3-sphere, analyzing circular thin positions and Seifert surfaces. Focuses on hyperbolic genus one knots with multiple disjoint Seifert surfaces, demonstrating their complex circular thin positions.
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1 Lesons
51 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore singular fibrations in knot exteriors and their extensions over handlebodies, connecting handle-ribbon knots to circular Morse functions in low-dimensional topology.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video