-
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
Tag Archives: surface subgroup
Surface subgroups of Sapir’s group
Let be the free group on two generators, and let be the endomorphism defined on generators by and . We define Sapir’s group to be the ascending HNN extension This group was studied by Crisp-Sageev-Sapir in the context of their … Continue reading
Posted in Ergodic Theory, Groups, Surfaces
Tagged f-folded surface, fatgraph, HNN extension, hyperbolic group, Sapir's group, Stallings folding, surface subgroup
12 Comments
Polygonal words
Last Friday, Henry Wilton gave a talk at Caltech about his recent joint work with Sang-hyun Kim on polygonal words in free groups. Their work is motivated by the following well-known question of Gromov: Question(Gromov): Let be a one-ended word-hyperbolic group. … Continue reading
Posted in Groups, Surfaces
Tagged double of free group, ends, Henry Wilton, hyperbolic groups, roundoff trick, Sang-hyun Kim, scl, Stallings theorem on ends, surface subgroup
6 Comments
