Stringy power operations in Tate K-theory

Abstract

We study the loop spaces of the symmetric powers of an orbifold and use our results to define equivariant power operations in Tate K-theory. We prove that these power operations are elliptic and that the Witten genus is an H_oo map. As a corollary, we recover a formula by Dijkgraaf, Moore, Verlinde and Verlinde for the orbifold Witten genus of these symmetric powers. We outline some of the relationship between our power operations and notions from (generalized) Moonshine.

This is the most recent (2008) version of this paper. Some part of the material (Devoto's Tate K-theory and the definition of power operations) has since been re-written for arXiv:1301.2754

References in corpus (3)

• Orbifolds as Groupoids: an Introduction
• Elliptic Algebras and Equivariant Elliptic Cohomology
• The loop orbifold of the symmetric product

Cited by in corpus (6)

• Quasi-elliptic cohomology and its Spectrum
• Twisted Equivariant Tate K-Theory
• Quasi-theories and their equivariant orthogonal spectra
• Almost Global Homotopy Theory
• Universal Finite Subgroup of the Tate Curve
• Transchromatic twisted character maps