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 ).
|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|
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