Small Cusped Hyperbolic 3-Manifolds and Order-Preserving Braids
Explore minimal-volume cusped hyperbolic 3-manifolds and their fundamental groups' orderability. Investigate order-preserving braids and their impact on Artin actions.
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.
Non-standard Orders on Torus Bundles with One Boundary
Explore non-standard bi-orderings of fundamental groups in torus bundles with one boundary, extending Perron-Rolfsen's work on standard orderings and Alexander polynomials.
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.
3-Manifold Groups and the Cannon Conjecture - Part I
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte. Examinez la conjecture de Cannon et ses variantes, ainsi que leurs connexions et critères.
Geometrization and its Consequences in 3-Manifold Topology - Part I
Explore Thurston's geometric perspective on 3-manifolds, including Perelman's Geometrization Theorem, and its implications for topology, algorithms, and group theory in 3-dimensional spaces.
Geometrization and Its Consequences in 3-Manifold Topology - Part II
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology. Discover algorithmic and group-theoretic applications in 3-manifold theory.
Geometrization and its Consequences in 3-Manifold Topology - Lecture 4
Explore hyperbolic geometry's role in 3-manifold topology, including Thurston's viewpoint and Perelman's theorem. Discover algorithmic and group-theoretic applications in computational experiments.
3-Manifold Groups and Fundamental Group Conjectures - Part II
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall et leurs interconnexions.
Division, Group Rings, and Negative Curvature in Low-Dimensional Topology
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.
Geometrization and its Consequences in 3-Manifold Topology - Lecture 3
Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology, algorithms, and group theory in 3D geometry.
An Approach to Simon's Conjecture
Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.
3-Manifold Groups and Fundamental Group Conjectures - Lecture 3
Explorez les conditions conjecturales impliquant qu'un groupe est le groupe fondamental d'une 3-variété compacte, en examinant les conjectures de Cannon et Wall ainsi que leurs interconnexions.
Ricci Limit Spaces are Semi-Locally Simply Connected
Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
The Thurston Norm of 3-Manifolds with a 2-Generator Fundamental Group
Explore the Thurston norm in 3-manifolds with 2-generator fundamental groups, delving into advanced concepts in quantum topology and geometric group theory.
Low Dimensional Topology and Circle-valued Morse Functions
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.
Low Dimensional Topology and Circle-valued Morse Functions
Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.