-
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
tiktok downloader on Bing’s wild involution Groups for which qua… on Big mapping class groups and… Anonymous on Stiefel-Whitney cycles as… Anonymous on Stiefel-Whitney cycles as… Israel Socratus Sado… on Bing’s wild involution 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: Hyperbolic geometry
Schläfli – for lush, voluminous polyhedra
Because of some turbulence in real life (™) over the last few months, it’s been somewhat hard to concentrate on research. Fortunately the obligation of teaching sometimes exerts the right sort of psychological pressure to keep my mind on mathematics in short bursts. Continue reading
Mr Spock complexes (after Aitchison)
The recent passing of Leonard Nimoy prompts me to recall a lesser-known connection between the great man and the theory of (cusped) hyperbolic 3-manifolds, observed by my friend and former mentor Iain Aitchison. In particular, I am moved to give a brief presentation … Continue reading
Mapping class groups: the next generation
Nothing stands still except in our memory. – Phillipa Pearce, Tom’s Midnight Garden In mathematics we are always putting new wine in old bottles. No mathematical object, no matter how simple or familiar, does not have some surprises in store. My … Continue reading
Groups quasi-isometric to planes
I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the … Continue reading
A tale of two arithmetic lattices
For almost 50 years, Paul Sally was a towering figure in mathematics education at the University of Chicago. Although he was 80 years old, and had two prosthetic legs and an eyepatch (associated with the Type 1 diabetes he had his … Continue reading
Posted in Hyperbolic geometry, Number theory
Tagged arithmetic lattice, Hyperbolic geometry, orthogonal group
2 Comments
3-manifolds everywhere
When I started in graduate school, I was very interested in 3-manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3-manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading
Posted in 3-manifolds, Groups, Hyperbolic geometry
Tagged 3-manifolds, acylindrical, quasiconvex group, Random groups, Sierpinski carpet
9 Comments
kleinian, a tool for visualizing Kleinian groups
It’s been a while since I last blogged; the reason, of course, is that I felt that I couldn’t post anything new before completing my series of posts on Kähler groups; but I wasn’t quite ready to write my last … Continue reading
Geometry and the imagination 