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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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