Cellular sheaf cohomology in Polymake

Abstract

This is a guide to the polymake extension cellularSheaves. We first define cellular sheaves on polyhedral complexes in Euclidean space, as well as cosheaves, and their (co)homologies. As motivation, we summarize some results from toric and tropical geometry linking cellular sheaf cohomologies to cohomologies of algebraic varieties. We then give an overview of the structure of the extension cellularSheaves for polymake. Finally, we illustrate the usage of the extension with examples from toric and tropical geometry.