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

Posted in Algebraic Geometry, Complex analysis, Geometric structures, Lie groups | Tagged , , , , | 8 Comments

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

Posted in Foliations, Geometric structures, Lie groups | Tagged , , , | 1 Comment

The Hall-Witt identity

The purpose of this blog post is to try to give some insight into the “meaning” of the Hall-Witt 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 , , , | 1 Comment

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

Posted in Commentary, Euclidean Geometry, Groups, Hyperbolic geometry, Lie groups, Overview, Visualization | 5 Comments

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 , , , , , , | Leave a comment

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

Posted in Geometric structures, Lie groups, Symplectic geometry | Tagged , , , , , , | 2 Comments

Geometric structures on 1-manifolds

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

Posted in Lie groups | Tagged , , , , , , , , , , | 1 Comment