University of Illinois Urbana-Champaign

Quasi-elliptic cohomology

Huan, Zhen

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HUAN-DISSERTATION-2017.pdf

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

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
Date of Ingest
2017-08-10T19:14:31Z
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

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