Genera of Integer Representations and the Lyndon-Hochschild-Serre Spectral Sequence.pdf (447.52 kB)

Genera of Integer Representations and the Lyndon-Hochschild-Serre Spectral Sequence

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thesis
posted on 06.08.2021, 12:30 by Chris Karl NeufferChris Karl Neuffer
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 $\mathbb{Z}^{n}\rtimes$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.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

Indianapolis

Advisor/Supervisor/Committee Chair

Daniel Ramras

Additional Committee Member 2

Ronghui Ji

Additional Committee Member 3

Patrick Morton

Additional Committee Member 4

Olguta Buse