Twisted Real quasi-elliptic cohomology

TL;DR

This paper develops a new twisted Real quasi-elliptic cohomology theory based on loop groupoids, incorporating symmetries like loop rotation and reflection, and explores its properties and connections to elliptic curves.

Contribution

It introduces the construction of twisted Real quasi-elliptic cohomology and develops related Pontryagin characters and string power operations.

Findings

Established basic properties of the new cohomology theory

Constructed twisted elliptic Pontryagin characters

Explored connections to the Tate curve

Abstract

In this paper we construct twisted Real quasi-elliptic cohomology as the twisted KR-theory of loop groupoids. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we construct twisted elliptic Pontryagin characters and, without twists, Real analogues of the string power operation of quasi-elliptic cohomology. We also explore the relation of the theory to the Tate curve.