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
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.
Recommended Citation
Lin, Matthew, "Graph Cohomology" (2016). HMC Senior Theses. 82.
https://scholarship.claremont.edu/hmc_theses/82
Source Fulltext
https://www.math.hmc.edu/~mlin/thesis/mlin-2016-thesis.pdf
