Quasi-elliptic cohomology

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

Huan, Zhen

关键词: Quasi-elliptic cohomology;    Tate K-theory;    Power operation;    Spectra;    Global homotopy theory;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/97268/HUAN-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.