Monday, September 30th, 2002
2:30pm - 3:30pm, in Science 2-065

Ethan Bolker

UMass Boston

How Is a Graph Like a Manifold?

Abstract: Some recent developments in the theory of group actions on complex manifolds have revealed unexpected connections between the geometry of these manifolds and the combinatorics of graphs immersed in n-space. In this talk I will discuss some of those connections, concentrating on the questions in combinatorics that come from the topology. In particular, I will explore conditions under which it makes sense to talk about the "Betti numbers" of an immersed graph. We can then use those Betti numbers to approach a proof of the McMullen conjectures for simple polytopes and to count the number of parallel redrawings of a framework.