English

Stringy power operations in Tate K-theory

Algebraic Topology 2013-01-22 v4 Mathematical Physics math.MP

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.

Cite

@article{arxiv.math/0701565,
  title  = {Stringy power operations in Tate K-theory},
  author = {Nora Ganter},
  journal= {arXiv preprint arXiv:math/0701565},
  year   = {2013}
}

Comments

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