Quasi-elliptic cohomology

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Huan, Zhen

Contributors dc:contributor

• Rezk, Charles
• McCarthy, Randy
• Ando, Matthew
• Stojanoska, Vesna

• Quasi-elliptic cohomology
• Tate K-theory
• Power operation
• Spectra
• Global homotopy theory

Statement dc:rights

• Copyright 2017 Zhen Huan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/97268

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/97268