Title

Graph Cohomology

Graduation Year

2016

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Dagan Karp

Reader 2

Satyan L. Devadoss

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

2016 Matthew S Lin

Abstract

What is the cohomology of a graph? Cohomology is a topological invariant and encodes such information as genus and euler characteristic. Graphs are combinatorial objects which may not a priori admit a natural and isomorphism invariant cohomology ring. In this project, given any finite graph G, we constructively define a cohomology ring H*(G) of G. Our method uses graph associahedra and toric varieties. Given a graph, there is a canonically associated convex polytope, called the graph associahedron, constructed from G. In turn, a convex polytope uniquely determines a toric variety. We synthesize these results, and describe the cohomology of the associated variety directly in terms of the graph G itself.