
Recent Posts
 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 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
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 Schläfli – for lush, vol… ianagol on Schläfli – for lush, vol… Danny Calegari on Schläfli – for lush, vol… ianagol on Schläfli – for lush, vol… Sunny on Explosions – now in glor… Categories
 3manifolds (20)
 4manifolds (2)
 Algebraic Geometry (2)
 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 (5)
 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 lesserknown connection between the great man and the theory of (cusped) hyperbolic 3manifolds, 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 quasiisometric 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
3manifolds everywhere
When I started in graduate school, I was very interested in 3manifolds, especially Thurston’s geometrization conjecture. Somehow in dimension 3, there is a marvelous marriage of flexibility and rigidity: generic 3manifolds are flexible enough to admit hyperbolic structures — i.e. Riemannian metrics … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry
Tagged 3manifolds, acylindrical, quasiconvex group, Random groups, Sierpinski carpet
Leave a comment