Genera of integer representations and the Lyndon-Hochschild-Serre spectral sequence

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Date
2021-08
Language
American English
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Ph.D.
Degree Year
2021
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Mathematical Sciences
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Purdue University
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Abstract

There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form Zn⋊G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan asks for suitable conditions for the Lyndon-Hochschild-Serre Spectral Sequence associated to this group extension to collapse at second page of the Lyndon-Hochschild-Serre spectral sequence. In this thesis we use facts from integer representation theory to reduce this problem to only considering representatives from each genus of representations, and establish techniques for constructing new examples in which the spectral sequence collapses.

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Indiana University-Purdue University Indianapolis (IUPUI)
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