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Rezk, Charles McCarthy, Randy Ando, Matthew Stojanoska, Vesna Huan, Zhen 2017-08-10T19:14:31Z 2017-08-10T19:14:31Z 2017-04-21 2017-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms The student, Zhen Huan, accepted the attached license on 2017-03-09 at 16:04. The student, Zhen Huan, submitted this Dissertation for approval on 2017-03-09 at 16:24. This Dissertation was approved for publication on 2017-04-21 at 10:39. DSpace SAF Submission Ingestion Package generated from Vireo submission #10583 on 2017-08-10 at 13:37:55 Made available in DSpace on 2017-08-10T19:14:31Z (GMT). No. of bitstreams: 3 HUAN-DISSERTATION-2017.pdf: 1951537 bytes, checksum: a4dccc00834b07e33ffa3a2d04545c6c (MD5) LICENSE.txt: 4206 bytes, checksum: d8dc0f44f4a1d062e69f7da37c82b916 (MD5) PROQUEST_LICENSE.txt: 4552 bytes, checksum: 629777c5455fa487e87e85105d8db6a4 (MD5) Previous issue date: 2017-04-21 application/pdf http://hdl.handle.net/2142/97268 en Copyright 2017 Zhen Huan Quasi-elliptic cohomology Tate K-theory Power operation Spectra Global homotopy theory Quasi-elliptic cohomology text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.