Power operations preserve Thom classes in twisted equivariant Real K-theory
Daniel Berwick-Evans, Meng Guo
TL;DR
This paper develops power operations in twisted equivariant Real K-theory for topological stacks, demonstrating they preserve Thom classes and commute with the twisted Atiyah-Bott-Shapiro orientation, advancing the understanding of algebraic structures in this context.
Contribution
It introduces power operations for twisted KR-theory of topological stacks and proves they preserve Thom classes and commute with key orientations, a novel advancement.
Findings
Power operations preserve universal Thom classes.
Twisted Atiyah-Bott-Shapiro orientation commutes with power operations.
Establishes algebraic properties of Clifford algebras in this setting.
Abstract
We construct power operations for twisted KR-theory of topological stacks. Standard algebraic properties of Clifford algebras imply that these power operations preserve universal Thom classes. As a consequence, we show that the twisted Atiyah-Bott-Shapiro orientation commutes with power operations.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models