
Recent Posts
 Taut foliations and positive forms
 Explosions – now in glorious 2D!
 Dipoles and Pixie Dust
 Mapping class groups: the next generation
 Groups quasiisometric to planes
 Div, grad, curl and all this
 A tale of two arithmetic lattices
 3manifolds 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
 Kenyon’s squarespirals
 Thurston talks on geometrization at Harvard
 Random turtles in the hyperbolic plane
 Surface subgroups of Sapir’s group
 Upper curvature bounds and CAT(K)
 Bill Thurston 19462012
Blogroll
 0xDE
 Area 777
 Combinatorics and more
 Deep street soul
 Evaluating EDiscovery
 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
 Mathematics under the microscope
 nCategory Cafe
 Noncommutative geometry
 Paul Krugman
 Persiflage
 Preposterous Universe
 Questionable content
 Quomodocumque
 Real Climate
 Scott McCloud
 Secret blogging seminar
 Sketches of topology
 T Calegari
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
Danny Calegari on Explosions – now in glor… rpotrie on Explosions – now in glor… Ferran on Mapping class groups: the next… Danny Calegari on Dipoles and Pixie Dust Laura DeMarco on Dipoles and Pixie Dust Categories
 3manifolds (18)
 4manifolds (2)
 Algebraic Geometry (2)
 Biology (2)
 Commentary (4)
 Complex analysis (9)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (12)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (5)
 Groups (31)
 Hyperbolic geometry (22)
 Knot theory (1)
 Lie groups (8)
 Number theory (1)
 Overview (2)
 Polyhedra (2)
 Probability (1)
 Projective geometry (1)
 Psychology (3)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (1)
 Surfaces (19)
 Symplectic geometry (3)
 TQFT (1)
 Uncategorized (5)
 Visualization (10)
Meta
Monthly Archives: May 2009
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
five week plan
As an experiment, I plan to spend the next five weeks documenting my current research on this blog. This research comprises several related projects, but most are concerned in one way or another with the general program of studying the … Continue reading
Posted in Overview
Tagged Gromov's question, hyperbolic groups, scl, stable commutator length, surface groups
4 Comments
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 wellknown problem in geometric group theory. Simply stated, the problem is as follows. Conjecture (Hanna Neumann): … Continue reading →