An Euler relation for valuations on polytopes

Michael Slone

Friday, March 5, 2004
11:00 am, 845 Patterson Office Tower

Abstract:

A given polytope is the projection of a simplicial complex called its visibility complex. We can use the visibility complex to study the combinatorial structure of the original polytope. In this talk we show that there is a family of inversion relations on polytopal valuations which generalize those of Euler and Dehn-Sommerville. We also apply the inversion relations to specific polytopal valuations, such as volume and surface area.