-
Recent Posts
- Bing’s wild involution
- Stiefel-Whitney cycles as intersections
- Schläfli – for lush, voluminous polyhedra
- Slightly elevated Teichmuller theory
- Mr Spock complexes (after Aitchison)
- Roots, Schottky semigroups, and Bandt’s Conjecture
- Taut foliations and positive forms
- Explosions – now in glorious 2D!
- Dipoles and Pixie Dust
- Mapping class groups: the next generation
- Groups quasi-isometric to planes
- Div, grad, curl and all this
- A tale of two arithmetic lattices
- 3-manifolds everywhere
- kleinian, a tool for visualizing Kleinian groups
- Kähler manifolds and groups, part 2
- Kähler manifolds and groups, part 1
- Liouville illiouminated
- Scharlemann on Schoenflies
- You can solve the cube – with commutators!
- Chiral subsurface projection, asymmetric metrics and quasimorphisms
- Random groups contain surface subgroups
- wireframe, a tool for drawing surfaces
- Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
- Orthocentricity
Blogroll
- 0xDE
- Area 777
- Bluefawnpinkmanga
- Combinatorics and more
- Deep street soul
- Evaluating E-Discovery
- floerhomology
- Gaddeswarup
- Geometric Group Theory
- Godel's lost letter and P=NP
- Images des mathematiques
- Jim Woodring
- Language Log
- Letters of note
- Low dimensional topology
- Math Overflow
- Math/Art Blog
- Mathematics under the microscope
- n-Category Cafe
- Noncommutative geometry
- Paul Krugman
- Persiflage
- Preposterous Universe
- Questionable content
- Quomodocumque
- Real Climate
- Scott McCloud
- Secret blogging seminar
- Sketches of topology
- Tanya Khovanova
- Terry Tao
- Tim Gowers
- Tony Phillips
Books
Software
Recent Comments
Anton Izosimov on How to see the genus Adam Wood on How to see the genus Constancy of the spe… on Measure theory, topology, and… Torsten on Circle packing – theory… aveliz on Second variation formula for m… Categories
- 3-manifolds (21)
- 4-manifolds (2)
- Algebraic Geometry (2)
- Algebraic Topology (1)
- Biology (2)
- Commentary (4)
- Complex analysis (11)
- Convex geometry (2)
- Diophantine approximation (1)
- Dynamics (13)
- Ergodic Theory (8)
- Euclidean Geometry (8)
- Foliations (2)
- Geometric structures (6)
- Groups (31)
- Hyperbolic geometry (25)
- Knot theory (1)
- Lie groups (8)
- Number theory (2)
- Overview (2)
- Polyhedra (3)
- Probability (1)
- Projective geometry (2)
- Psychology (3)
- Riemannian geometry (1)
- Rigidity (2)
- Special functions (2)
- Surfaces (20)
- Symplectic geometry (3)
- TQFT (1)
- Uncategorized (6)
- Visualization (10)
Meta
Category Archives: Groups
Groups with free subgroups
More ambitious than simply showing that a group is infinite is to show that it contains an infinite subgroup of a certain kind. One of the most important kinds of subgroup to study are free groups. Hence, one is interested … Continue reading
Posted in Groups
Tagged amenable groups, free groups, hyperbolic groups, laws, pingpong, Thompson's group, Tits alternative, von Neumann conjecture
3 Comments
Infinite groups
Before looking for surface subgroups, it is worth thinking about how to find (or rule out the existence of) simpler classes of subgroups. This is a very general question, and I do not intend to give a complete survey; however, … Continue reading
The (strengthened) Hanna Neumann Conjecture
A few days ago, Joel Friedman posted a paper on the arXiv purporting to give a proof of the (strengthened) Hanna Neumann conjecture, a well-known problem in geometric group theory. Simply stated, the problem is as follows. Conjecture (Hanna Neumann): … Continue reading →