Quasi-elliptic cohomology

Huan, Zhen

Permalink

https://hdl.handle.net/2142/97268 Copy

Description

Title

Quasi-elliptic cohomology

Author(s)

Huan, Zhen

Issue Date

2017-04-21

Director of Research (if dissertation) or Advisor (if thesis)

Rezk, Charles

Doctoral Committee Chair(s)

McCarthy, Randy

Committee Member(s)

• Ando, Matthew
• Stojanoska, Vesna

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2017-05

Type of Resource

text

Permalink

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

Copyright and License Information

Copyright 2017 Zhen Huan

Owning Collections