Cohomology of Certain Polyhedral Product Spaces

Author

Elizabeth A. Vidaurre, CUNY Graduate CenterFollow

Date of Degree

6-2016

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy

Program

Mathematics

Advisor

Martin Bendersky

Committee Members

Martin Bendersky

Abhijit Champanerkar

Robert Thompson

Subject Categories

Geometry and Topology

Keywords

toric topology, real moment-angle complexes, polyhedral products, composed simplicial complexes

Abstract

The study of torus actions led to the discovery of moment-angle complexes and their generalization, polyhedral product spaces. Polyhedral products are constructed from a simplicial complex. This thesis focuses on computing the cohomology of polyhedral products given by two different classes of simplicial complexes: polyhedral joins (composed simplicial complexes) and $n$-gons. A homological decomposition of a polyhedral product developed by Bahri, Bendersky, Cohen and Gitler is used to derive a formula for the case of polyhedral joins. Moreover, methods from and results by Cai will be used to give a full description of the non-trivial cup products in a real moment-angle manifold over a $n$-gon in terms of the combinatorial generators.

Recommended Citation

Vidaurre, Elizabeth A., "Cohomology of Certain Polyhedral Product Spaces" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1271