A Mathematics Colloquium

  • Published 2016

Abstract

Abstract: Euler’s formula, V −E+F = 2, places restrictions on the set of all vectors (V,E, F ) that can appear when counting the number of vertices, edges, and faces in a planar graph. Similarly, the orientability and Euler characteristic of a surface completely characterize the combinatorial structure of any triangulation of that surface. In this talk, I will discuss generalizations of these results to triangulations of higher-dimensional manifolds. The goal will be to address the question: “What can be said about the number of vertices, edges, triangles, etc., in a triangulated d-manifold?” Along the way, I will introduce some simple yet powerful algebraic tools that can be used to help answer this question that is rooted in combinatorial topology.

Cite this paper

@inproceedings{2016AMC, title={A Mathematics Colloquium}, author={}, year={2016} }