Twisted Real quasi-elliptic cohomology
Zhen Huan, Matthew B. Young

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models
