Ruys De Perez, Alexander Mark (2021-04). New Tools for Classifying Convex Neural Codes: The Factor Complex and the Wheel. Doctoral Dissertation.
Thesis
The neural code has prompted many questions in pure mathematics concerning how much topological data can be stored combinatorially. The question of whether one can determine the convexity of a neural code is particularly prominent. In this dissertation, we provide new tools toward answering this question. First, we introduce a related object called the factor complex, and show how it encodes a property of the neural code called max-intersection-completeness. Second, we introduce a new type of nonconvex phenomenon called a wheel, and show how to read it combinatorially.
