Distances in the homology curve complex

Geometry Topology Seminar
Tuesday, May 31, 2011 - 13:05
1 hour (actually 50 minutes)
Skiles 006
U Bonn
In this talk a curve complex HC(S) closely related to the "Cyclic Cycle Complex" (Bestvina-Bux-Margalit) and the "Complex of Cycles" (Hatcher) is defined for an orientable surface of genus g at least 2. The main result is a simple algorithm for calculating distances and constructing quasi-geodesics in HC(S). Distances between two vertices in HC(S) are related to the "Seifert genus" of the corresponding link in S x R, and behave quite differently from distances in other curve complexes with regards to subsurface projections.