
Recent Posts
 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
 Circle packing – theory and practice
 Agol’s Virtual Haken Theorem (part 3): return of the hierarchies
 Agol’s Virtual Haken Theorem (part 2): AgolGrovesManning strike back
Blogroll
 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
Categories
 3manifolds (17)
 4manifolds (2)
 Algebraic Geometry (2)
 Biology (2)
 Commentary (4)
 Complex analysis (8)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (10)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (1)
 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 (2)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (1)
 Surfaces (19)
 Symplectic geometry (2)
 TQFT (1)
 Uncategorized (5)
 Visualization (9)
Meta
Tag Archives: surface groups
Surface subgroups – more details from Jeremy Kahn
Jeremy Kahn kindly sent me a more detailed overview of his argument with Vlad Markovic, that I blogged earlier about here (also see Jesse Johnson’s blog for other commentary). With his permission, this is reproduced below in its entirety. Editorial … Continue reading
Posted in 3manifolds, Ergodic Theory, Surfaces
Tagged Kahn, Markovic, pair of pants, surface groups
4 Comments
Surface subgroups in hyperbolic 3manifolds
I just learned from Jesse Johnson’s blog that Vlad Markovic and Jeremy Kahn have announced a proof of the surface subgroup conjecture, that every complete hyperbolic manifold contains a closed injective surface. Equivalently, contains a closed surface subgroup. Apparently, Jeremy … Continue reading
Posted in 3manifolds, Ergodic Theory, Surfaces
Tagged Bowen, geodesic flow, Hall's marriage theorem, Kahn, LERF, Markovic, pair of pants, surface groups, Waldhausen
10 Comments
Groups with free subgroups (part 2)
In a previous post, I discussed some methods for showing that a given group contains a (nonabelian) free subgroup. The methods were analytic and/or dynamical, and phrased in terms of the existence (or nonexistence) of certain functions on or on … 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