Santa Clara University

Speaker: Eric Babson, UC Davis

Tuesday May 24, O'Connor 207

Title: Complexes with few triangles and random groups

Abstract: If every subcomplex of a two dimensional simplicial complex has too few triangles to be a torus then the complex has the topological type of some circles, spheres and projective planes. This topological fact arises in the study of random complexes and turns out to control the behavior of the fundamental group. The analogous situation in which the subcomplexes have too few edges to be a torus is not understood. This type of complex occurs in the study of clique complexes of random graphs and the analogous topological restriction would yield results about their fundamental groups.