Combinatorial Geodesics in Triangle-Square Complexes

Start: 04/28/2010 - 4:15pm
End  : 04/28/2010 - 5:15pm


Rena Levitt, Pomona College


It is a well understood principle in geometric group theory that there is a close connection between the coarse geometry of the universal cover of a compact topological space and the computational properties of its fundamental group. This connection is especially strong when the space admits a non positively curved metric. Thus one method to study the computation properties of the fundamental groups of non positively curved spaces is to look at the paths in the universal cover of the space. In this talk, I will concentrate on the class of non positively curved triangle-square complexes, where the set of paths we consider are combinatorial geodesics. Somewhat surprisingly, combinatorial geodesics in mixed complexes do not share many of the properties of those in pure triangle or in pure square complexes. I will outline the key differences. Then I will define a set of canonical paths we hope will be the basis for answering computational questions for groups acting on non positively curved triangle-square complexes. This is ongoing work with Jon McCammond.

Beckman B126, Harvey Mudd College

Misc. Information

Refreshments will be served at 3:45 p.m in Olin B16, Harvey Mudd College
The dinner will be hosted by Prof. Asuman G. Aksoy.
If interested in attending, please call ext. 72769