Steve Klee

Euler’s formula,V−E+F= 2, places restrictionson the set of all vectors (V, E, F) that can appear when count-ing the number of vertices, edges, and faces in a planar graph.Similarly, the orientability and Euler characteristic of a surfacecompletely characterize the combinatorial structure of any tri-angulation of that surface. In this talk, I will discuss general-izations of these results to triangulations of higher-dimensionalmanifolds. The goal will be to address the question: “What canbe said about the number of vertices, edges, triangles, etc., in atriangulatedd-manifold?” Along the way, I will introduce somesimple yet powerful algebraic tools that can be used to helpanswer this question that is rooted in combinatorial topology.