Twisted Equivariant Tate K-Theory

Thomas Dove

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arXiv · 1912.02374

Twisted Equivariant Tate K-Theory

Thomas Dove

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Abstract

Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$. This gives a loop based definition of twisted equivariant Tate K-theory for finite groups that conforms to the definition that Luecke provides for compact, connected Lie groups. We relate our construction to Ganter's work on Moonshine and Huan's quasi-elliptic cohomology.

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Thomas Dove. 2019-12-05. Twisted Equivariant Tate K-Theory. https://arxiv.org/abs/1912.02374

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