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 Bing’s wild involution
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 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
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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
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Category Archives: Uncategorized
Bing’s wild involution
An embedded circle separates the sphere into two connected components; this is the Jordan curve theorem. A strengthening of this fact, called the JordanSchoenflies theorem, says that the two components are disks; i.e. every embedded circle in the sphere bounds a … Continue reading
Posted in 3manifolds, Uncategorized
Tagged Alexander horned sphere, Bing, wild involution
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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
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
Hyperbolic Geometry Notes #5 – Mostow Rigidity
1. Mostow Rigidity For hyperbolic surfaces, Moduli space is quite large and complicated. However, in three dimensions Moduli space is trivial: Theorem 1 If is a homotopy equivalence of closed hyperbolic manifolds with , then is homotopic to an isometry. … Continue reading
Posted in 3manifolds, Groups, Hyperbolic geometry, Uncategorized
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Hyperbolic Geometry Notes #2 – Triangles and Gauss Bonnet
In this post, I will cover triangles and area in spaces of constant (nonzero) curvature. We are focused on hyperbolic space, but we will talk about spheres and the GaussBonnet theorem. 1. Triangles in Hyperbolic Space Suppose we are given … Continue reading
Bill Thurston 19462012
This morning I heard the awful news that Bill Thurston died last night. Many of us knew that Bill was very ill, but we all hoped (or imagined?) that he would still be with us for a while yet, and … Continue reading →