Tag Archives: CAT(K)

Mr Spock complexes (after Aitchison)

The recent passing of Leonard Nimoy prompts me to recall a lesser-known connection between the great man and the theory of (cusped) hyperbolic 3-manifolds, observed by my friend and former mentor Iain Aitchison. In particular, I am moved to give a brief presentation … Continue reading

Posted in 3-manifolds, Hyperbolic geometry, Polyhedra | Tagged , , , , , , | Leave a comment

Upper curvature bounds and CAT(K)

I am currently teaching a class at the University of Chicago on hyperbolic groups, and I have just introduced the concept of -hyperbolic (geodesic) metric spaces. A geodesic metrix space is -hyperbolic if for any geodesic triangle , and any … Continue reading

Posted in Hyperbolic geometry, Surfaces | Tagged , , , , , | 2 Comments