On Matveev’s Complexity of Classical and Virtual 3 Manifolds
Explore Matveev's complexity theory for classical and virtual 3-manifolds, delving into advanced topological concepts and their applications in quantum topology.
Cohomological Donaldson-Thomas Invariants of 3-Manifolds - Part 2
Explore Morse homology of complex Chern-Simons functional, its connections to supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
Cohomological Donaldson-Thomas Invariants of 3-Manifolds
Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.
Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology
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.
Anosov Flows on 3-Manifolds
Explore Anosov flows on 3-manifolds, delving into advanced concepts in dynamical systems and topology presented by Katie Mann.
The Genus-One Question for Open Book Decomposition in Contact Structures and Anosov Flows
Explore the genus-one question for open book decomposition in 3D contact structures and Anosov flows, examining constructions and partial results.
Turaev-Viro-Barrett-Westbury State Sums with Defects
Explore Turaev-Viro-Barrett-Westbury state sums with defects in quantum field theory, presented by C. Meusburger from Friedrich-Alexander-Universität.
Recent Inequalities on the Mass-to-Capacity Ratio
Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
On Exotic Embeddings of Submanifolds in 4-Manifolds
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.
Categorification of Quantum Invariants: From Knots to 3-Manifolds - Part 1
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.
On the Structure of Skein Modules
Explore Kauffman bracket skein modules, examining conjectures and theorems. Discover counterexamples and new insights into the structure of these modules in 3-manifolds.
Orderability of 3-Manifold Groups and the L-Space Conjecture
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.
Detecting 3-Manifold Groups Among Circularly Ordered Groups
Explore techniques for identifying 3-manifold groups within circularly ordered groups, focusing on mathematical detection methods and group theory applications.
Left-Orderability and Toroidal 3-Manifolds
Explore left-orderability in 3-manifolds with incompressible tori, using order-detection of slopes. Gain insights into the L-space conjecture through new evidence.
Finite Quotients of Fibered, Cusped 3-Manifold Groups
Explore finite quotients of 3-manifold groups, leveraging mapping class group properties to study profinite completions of fibered hyperbolic 3-manifold fundamental groups.
Rank of 3-Manifold Groups - Part I
Explore 3-manifold group ranks, covering generation, Heegaard genus, growth in cover towers, mapping tori, and geometric decompositions of hyperbolic 3-manifolds.
Algebraization of Low-Dimensional Topology - Part II
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Hyperbolic Manifolds in Dimension Higher Than 3
Explore hyperbolic manifolds in dimensions 4 and higher, examining their properties, challenges in description, and current understanding in topology.
A Combinatorial Characterization of Geometric 3-Manifolds - Lecture
Explore geometric 3-manifolds through combinatorial characterization, focusing on Thurston geometries and their local combinatorial definitions. Learn about new algorithms for geometric decomposition.
Virtually Free-by-Cyclic Groups
Explore recognition methods for virtually free-by-cyclic groups within hyperbolic compact special groups using homology techniques.
Subgroup Separability of 3-Manifold Groups and Its Applications
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.