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.

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