Cohomology of Certain Polyhedral Product Spaces

Author

Elizabeth A. Vidaurre, Graduate Center, City University of New YorkFollow

Date of Degree

6-2016

Document Type

Dissertation

Degree Name

Ph.D.

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