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 kleinian, a tool for visualizing Kleinian groups
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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
 Agol’s Virtual Haken Theorem (part 1)
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Category Archives: Visualization
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
wireframe, a tool for drawing surfaces
The purpose of this brief blog post is to advertise that I wrote a little piece of software called wireframe which can be used to quickly and easily produce .eps figures of surface for inclusion in papers. The main use is … Continue reading
Random turtles in the hyperbolic plane
My eldest daughter Lisa recently brought home a note from her school from her computer class teacher. Apparently, the 5th grade kids have been learning to program in Logo, in the MicroWorlds programming environment. I have very pleasant memories of … Continue reading
Circle packing – theory and practice
I am spending a few months in Göttingen as a Courant Distinguished Visiting Professor, and talking a bit to Laurent Bartholdi about rational functions — i.e. holomorphic maps from the Riemann sphere to itself. A rational function is determined (up … 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
1 Comment
Imagining the plane
The other day at lunch, one of my colleagues — let’s call her “Wendy Hilton” to preserve her anonymity (OK, this is pretty bad, but perhaps not quite as bad as Clive James’s use of “Romaine Rand” as a pseudonym … Continue reading
Posted in Biology, Psychology, Visualization
Tagged Cartesian coordinates, Moore's axioms, the plane, Zariski topology
3 Comments
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 →