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 Groups quasiisometric to planes
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 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
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Category Archives: Hyperbolic geometry
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
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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
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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
Chiral subsurface projection, asymmetric metrics and quasimorphisms
Last week I was at Oberwolfach for a meeting on geometric group theory. My friend and collaborator Koji Fujiwara gave a very nice talk about constructing actions of groups on quasitrees (i.e. spaces quasiisometric to trees). The construction is inspired … Continue reading
Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
There is an old puzzle which starts by asking: what is the next number in the sequence 1,2,4,? We are supposed to recognize the start of the sequence and answer that the next number is surely 8, because the first … Continue reading
Thurston talks on geometrization at Harvard
In winter and spring of 2001, Nathan Dunfield and I ran a seminar at Harvard whose purpose was to go through Thurston’s proof of the geometrization theorem for Haken manifolds. This was a very useful and productive exercise, and there … Continue reading