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#3-Manifolds

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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
Simons Semester on Dynamics

Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 1

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Explore dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analog for surface diffeomorphisms. Delve into connections with Teichmüller Theory and 3-manifold topology.
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1 Lesons
1 hour 40 minutes
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Simons Semester on Dynamics

Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 3

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Explore dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analogue for surface diffeomorphisms. Delve into connections with Teichmüller Theory and 3-manifold topology.
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1 Lesons
57 minutes
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Simons Semester on Dynamics

Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 2

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Explore models for dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analogue for surface diffeomorphisms.
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1 Lesons
1 hour 31 minutes
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Centre de recherches mathématiques - CRM

Dynamics to Geometry in Free-by-Cyclic Groups - Lecture 3

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Explorez les liens entre dynamique, algèbre et géométrie dans les groupes libres-par-cycliques. Découvrez les résultats récents et les problèmes ouverts dans ce domaine inspiré par les travaux de Thurston.
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1 Lesons
50 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Dynamics to Geometry in Free-by-Cyclic Groups - Lecture 2

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Explore dynamics and geometry in free-by-cyclic groups, focusing on automorphisms, semi-direct products, and their interplay with Thurston's work on surface homeomorphisms and 3-manifolds.
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1 Lesons
55 minutes
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Centre de recherches mathématiques - CRM

Dynamics to Geometry in Free-by-Cyclic Groups - Part I

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Explore the interplay between automorphism dynamics, algebraic properties, and coarse geometry in free-by-cyclic groups, drawing inspiration from Thurston's work on surface homeomorphisms and 3-manifolds.
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1 Lesons
48 minutes
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Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Part I

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Explore algebraic presentations of cobordism categories in low-dimensional topology. Learn about 3- and 4-modular Hopf algebras and their role in classifying TQFTs.
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1 Lesons
57 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Complex Dynamics in the Tropics - Structures on 2- and 3-Manifolds Coming from Dynamical Systems

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Explore complex dynamics in the tropics, focusing on structures in 2- and 3-manifolds derived from dynamical systems. Gain insights into multimodal maps, hyperbolic groups, and related mathematical concepts.
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8 Lesons
43 minutes
On-Demand
Free-Video
IMSA

From Turaev to Rokhlin via VOA Characters and Curve Counting

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Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into Spin-C structures and related mathematical concepts.
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13 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

Bounds on Morse-Novikov Numbers of 3-Manifolds

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Explore bounds on Morse-Novikov numbers of 3-manifolds, examining circle-valued Morse functions and their critical points, with applications to knot theory and topology.
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17 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

From Turaev to Rokhlin via VOA Characters and Curve Counting

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Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into recent developments in this mathematical field.
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11 Lesons
1 hour 12 minutes
On-Demand
Free-Video
ICTP Mathematics

From Knots to Number Theory II

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Explore connections between quantum knot invariants and number theory, covering topics like hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
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13 Lesons
1 hour 21 minutes
On-Demand
Free-Video
ICTP Mathematics

Slope Detection in 3-Manifolds

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Explore key concepts in 3-manifold topology, including slope detection, Lagrangian theory, and foliations. Learn about conjectures, theorems, and algorithms in this advanced mathematical field.
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18 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
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IMSA

Braidings and Braid Equivalences

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Explore braiding algorithms and braid equivalences for various knot types, including classical, virtual, and singular, with a focus on knotoids and braidoids.
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1 Lesons
1 hour
On-Demand
Free-Video
International Mathematical Union

Jacob Rasmussen - Floer Homology of 3-Manifolds with Torus Boundary

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Explore advanced concepts in Floer homology, focusing on 3-manifolds with torus boundary. Gain insights into cutting-edge mathematical research and its applications in topology.
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1 Lesons
46 minutes
On-Demand
Free-Video
ICTP Mathematics

From Knots to Number Theory I

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Explore connections between quantum knot invariants and number theory, covering hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
QuantumTopology

Stable Maps and Branched Shadows of 3-Manifolds

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Explore stable maps and branched shadows in 3-manifolds, delving into advanced concepts in quantum topology and geometric structures.
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1 Lesons
48 minutes
On-Demand
Free-Video
QuantumTopology

Ph. Korablev - Skein-Invariants of 3-Manifolds

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Explore skein-invariants of 3-manifolds in this advanced topology lecture, delving into complex mathematical concepts and their applications in quantum topology.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
QuantumTopology

Calculation of Casson Invariant for 3-Manifolds

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Explore the calculation methods for Casson invariant in 3-manifolds, a crucial topological invariant in low-dimensional topology and knot theory.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
QuantumTopology

On Matveev’s Complexity of Classical and Virtual 3 Manifolds

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Explore Matveev's complexity theory for classical and virtual 3-manifolds, delving into advanced topological concepts and their applications in quantum topology.
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1 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Cohomological Donaldson-Thomas Invariants of 3-Manifolds - Part 2

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Explore Morse homology of complex Chern-Simons functional, its connections to supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
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1 Lesons
56 minutes
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IMSA

Cohomological Donaldson-Thomas Invariants of 3-Manifolds

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Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology

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Explore bordered Floer homology, dg-modules, and the topological interpretation of module homomorphism composition in Heegaard Floer complexes. Gain insights into cobordism maps and their consequences.
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1 Lesons
45 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Anosov Flows on 3-Manifolds

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Explore Anosov flows on 3-manifolds, delving into advanced concepts in dynamical systems and topology presented by Katie Mann.
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1 Lesons
57 minutes
On-Demand
Free-Video
Institut Henri Poincaré

The Genus-One Question for Open Book Decomposition in Contact Structures and Anosov Flows

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Explore the genus-one question for open book decomposition in 3D contact structures and Anosov flows, examining constructions and partial results.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
NCCR SwissMAP

Turaev-Viro-Barrett-Westbury State Sums with Defects

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Explore Turaev-Viro-Barrett-Westbury state sums with defects in quantum field theory, presented by C. Meusburger from Friedrich-Alexander-Universität.
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1 Lesons
1 hour 4 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Recent Inequalities on the Mass-to-Capacity Ratio

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Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
Stony Brook Mathematics

On Exotic Embeddings of Submanifolds in 4-Manifolds

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Explore exotic embeddings of submanifolds in 4-manifolds, focusing on phenomena that survive stabilizations. Delve into advanced 4-dimensional topology concepts and recent research findings.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Banach Center

Categorification of Quantum Invariants: From Knots to 3-Manifolds - Part 1

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Explore categorification of quantum invariants, focusing on knots and 3-manifolds. Delve into advanced mathematical concepts with expert Sergei Gukov from Caltech and Dublin IAS.
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1 Lesons
50 minutes
On-Demand
Free-Video
Banach Center

On the Structure of Skein Modules

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Explore Kauffman bracket skein modules, examining conjectures and theorems. Discover counterexamples and new insights into the structure of these modules in 3-manifolds.
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1 Lesons
54 minutes
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Centre de recherches mathématiques - CRM

Orderability of 3-Manifold Groups and the L-Space Conjecture

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Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Detecting 3-Manifold Groups Among Circularly Ordered Groups

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Explore techniques for identifying 3-manifold groups within circularly ordered groups, focusing on mathematical detection methods and group theory applications.
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1 Lesons
54 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Left-Orderability and Toroidal 3-Manifolds

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Explore left-orderability in 3-manifolds with incompressible tori, using order-detection of slopes. Gain insights into the L-space conjecture through new evidence.
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1 Lesons
57 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Finite Quotients of Fibered, Cusped 3-Manifold Groups

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Explore finite quotients of 3-manifold groups, leveraging mapping class group properties to study profinite completions of fibered hyperbolic 3-manifold fundamental groups.
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1 Lesons
42 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Rank of 3-Manifold Groups - Part I

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Explore 3-manifold group ranks, covering generation, Heegaard genus, growth in cover towers, mapping tori, and geometric decompositions of hyperbolic 3-manifolds.
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1 Lesons
57 minutes
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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
BIMSA

Hyperbolic Manifolds in Dimension Higher Than 3

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Explore hyperbolic manifolds in dimensions 4 and higher, examining their properties, challenges in description, and current understanding in topology.
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1 Lesons
1 hour 7 minutes
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Free-Video
Centre de recherches mathématiques - CRM

A Combinatorial Characterization of Geometric 3-Manifolds - Lecture

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Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.
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1 Lesons
52 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Virtually Free-by-Cyclic Groups

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Explore recognition methods for virtually free-by-cyclic groups within hyperbolic compact special groups using homology techniques.
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1 Lesons
47 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Subgroup Separability of 3-Manifold Groups and Its Applications

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Explore subgroup separability in 3-manifold groups, its characterization via torus decomposition, and applications to subgroup distortion and Grothendieck rigidity. Joint work with Hoang Thanh Nguye.
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1 Lesons
52 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
BIMSA

Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds

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Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
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1 Lesons
52 minutes
On-Demand
Free-Video
BIMSA

Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems

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Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
QuantumTopology

The Thurston Norm of 3-Manifolds with a 2-Generator Fundamental Group

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Explore the Thurston norm in 3-manifolds with 2-generator fundamental groups, delving into advanced concepts in quantum topology and geometric group theory.
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1 Lesons
52 minutes
On-Demand
Free-Video
IMSA

Floer Theory and Quantum Groups

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Explore Floer theory, quantum groups, and gauge theories in 3-manifolds. Discover connections between moduli spaces, Floer invariants, and skein modules in topological quantum field theory.
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1 Lesons
1 hour 3 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
BIMSA

Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds

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Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video