Graduation Year
2020
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Francis Edward Su
Reader 2
Dagan Karp
Terms of Use & License Information
Rights Information
2020 Savana Jade Ammons
Abstract
In this thesis, we develop a discrete analogue to the Poincaré–Hopf Theorem. We define the notion of a vector field on a graph, and establish an index theory for such a field. Specifically, we create well-defined indices for the nodes and “cells" formed by a planar graph. Then, we show that the sum of these indices remains constant for certain types of planar graphs, regardless of the discrete vector fields they have.
Recommended Citation
Ammons, Savana, "A Discrete Analogue for the Poincaré-Hopf Theorem" (2020). HMC Senior Theses. 237.
https://scholarship.claremont.edu/hmc_theses/237
COinS
