Cellular sheaves as a foundation for polymer embeddings

Abstract

Polymers can be represented by a graph, also known as a 1-dimensional cell complex. Since polymers exist in three-dimensional space, we wish to mathematically embed graphs into R3 (more generally Rd). Cohomology keeps track of the structure of our graph as we embed it. Building upon the framework developed by Cantarella et al. [1], we make a connection to the natural way of finding cohomology through the cohomology of the constant sheaf. Motivated by this perspective, we modify the constant sheaf to fit different embedding restrictions.