Cellular sheaf cohomology in Polymake

This chapter provides a guide to our 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 summarise some results from toric and tropical geometry linking cellular sheaf cohom...

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Bibliographic Details
Published in:arXiv.org 2016-12
Main Authors: Kastner, Lars, Shaw, Kristin, Winz, Anna-Lena
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Homology
Sheaves
Online Access:Get full text
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Summary:This chapter provides a guide to our 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 summarise 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.
ISSN:2331-8422