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 Liouville illiouminated
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 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
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 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: Lie groups
Kähler manifolds and groups, part 1
One of the nice things about living in Hyde Park is the proximity to the University of Chicago. Consequently, over the summer I came in to the department from time to time to work in my office, where I have … Continue reading
Characteristic classes of foliations
I recently learned from Jim Carlson’s blog of the passing of Harsh Pittie on January 16 this year. I never met Harsh, but he is very familiar to me through his work, in particular for his classic book Characteristic classes … Continue reading
The HallWitt identity
The purpose of this blog post is to try to give some insight into the “meaning” of the HallWitt identity in group theory. This identity can look quite mysterious in its algebraic form, but there are several ways of describing it geometrically which … Continue reading
Posted in Groups, Lie groups, Surfaces, Visualization
Tagged commutators, gropes, HallWitt identity, visualization
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FH, T, FLp and all that
I am (update: was) currently (update: but am no longer) in Brisbane for the “New directions in geometric group theory” conference, which has been an entirely enjoyable and educational experience. I got to eat fish and chips, to watch Australia … Continue reading
Posted in Groups, Lie groups, Rigidity
Tagged aTmenable, bounded cohomology, lattices, property FH, property FL_p, property T, universal lattice
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Causal geometry
On page 10 of Besse’s famous book on Einstein manifolds one finds the following quote: It would seem that Riemannian and Lorentzian geometry have much in common: canonical connections, geodesics, curvature tensor, etc. . . . But in fact this … Continue reading
Geometric structures on 1manifolds
A geometric structure on a manifold is an atlas of charts with values in some kind of “model space”, and transformation functions taken from some pseudogroup of transformations on the model space. If is the model space, and is the … Continue reading
Hyperbolic Geometry (157b) Notes #1
I am Alden, one of Danny’s students. Error/naivete that may (will) be found here is mine. In these posts, I will attempt to give notes from Danny’s class on hyperbolic geometry (157b). This first post covers some models for hyperbolic … Continue reading →