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Dissertation/Thesis Abstract

On the Structure of Polyhedral Products
by Das, Shouman, Ph.D., University of Rochester, 2020, 103; 28027019
Abstract (Summary)

In this thesis, we study the structure of the polyhedral product ZK(D1 , S0 ) determined by an abstract simplicial complex K and the pair (D1,S0). We showed that there is natural embedding of the hypercube graph in ZKn (D1 , S0) where Kn is the boundary of an n-gon. This also provides a new proof of a known theorem about genus of the hypercube graph. We give a description of the invertible natural transformations of the polyhedral product functor. Then, we study the action of the cyclic group ℤn on the space ZKn (D1 , S0) . This action determines Z[Zn]-module structure of the homology group H∗(ZKn (D1 , S0)). We also study the Leray-Serre spectral sequence associated to the homotopy orbit space EZn ×Zn ZKn (D1 , S0 ).

Indexing (document details)
Advisor: Cohen, Frederick R.
Commitee: Shapir, Yonathan, Pakianathan, Jonathan, Stefankovic, Daniel
School: University of Rochester
Department: School of Arts and Sciences
School Location: United States -- New York
Source: DAI-B 82/3(E), Dissertation Abstracts International
Subjects: Mathematics, Computer science, Engineering
Keywords: Graph genus, Homology, Homotopy orbit space, Hypercube graph, Polyhedral product
Publication Number: 28027019
ISBN: 9798664788075
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