"A variety of recent results concerning f-vectors of manifolds"

Isabella Novik
University of Washington

Monday, April 27, 2009
4:00 pm, 845 Patterson Office Tower

Abstract:

Given a simplicial complex, we can count the number of its vertices, edges, triangles, etc. These are called the face numbers of a complex. What can be said about the possible face numbers of various classes of simplicial complexes (e.g, simplicial polytopes, simplicial spheres, or, more generally, simplicial manifolds)? In this talk we will report on a recent progress on that question for simplicial manifolds. For the class of manifolds with polytopal links our results include the proof of (1) Kalai's manifold g-conjecture and (2) Kühnel's upper bound conjecture on the Betti numbers of manifolds. This is joint work with Ed Swartz.