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Title:Quasi-elliptic cohomology
Author(s):Huan, Zhen
Director of Research:Rezk, Charles
Doctoral Committee Chair(s):McCarthy, Randy
Doctoral Committee Member(s):Ando, Matthew; Stojanoska, Vesna
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Quasi-elliptic cohomology
Tate K-theory
Power operation
Spectra
Global homotopy theory
Abstract:We introduce and study quasi-elliptic cohomology, a theory related to Tate K-theory but built over the ring $\mathbb{Z}[q^{\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant Tate K-theory. In Chapter 3 we construct power operation in the orbifold theory, and prove a version of Strickland's theorem on symmetric equivariant cohomology modulo transfer ideals. In Chapter 4 we construct representing spectra but show that they cannot assemble into a global spectrum in the usual sense. In Chapter 6 we construct a new global homotopy theory containing the classical theory. In Chapter 7 we show quasi-elliptic cohomology is a global theory in the new category.
Issue Date:2017-04-21
Type:Thesis
URI:http://hdl.handle.net/2142/97268
Rights Information:Copyright 2017 Zhen Huan
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05


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