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Power operations in the Stolz–Teichner program

Tobias Barthel, Daniel Berwick-Evans and Nathaniel Stapleton

Geometry & Topology 26 (2022) 1773–1848

The Stolz–Teichner program proposes a deep connection between geometric field theories and certain cohomology theories. We extend this connection by developing a theory of geometric power operations for geometric field theories restricted to closed bordisms. These operations satisfy relations analogous to the ones exhibited by their homotopical counterparts. We also provide computational tools to identify the geometrically defined operations with the usual power operations on complexified equivariant K–theory. Further, we use the geometric approach to construct power operations for complexified equivariant elliptic cohomology.

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elliptic cohomology, supersymmetric field theories, equivariant K-theory, power operations, Stolz–Teichner program
Mathematical Subject Classification
Primary: 55N34, 81T60, 55S25
Received: 2 July 2020
Revised: 26 May 2021
Accepted: 27 June 2021
Published: 28 October 2022
Proposed: Mark Behrens
Seconded: Marc Levine, Stefan Schwede
Tobias Barthel
Max Planck Institute for Mathematics
Daniel Berwick-Evans
Department of Mathematics
University of Illinois at Urbana–Champaign
Urbana, IL
United States
Nathaniel Stapleton
Department of Mathematics
University of Kentucky
Lexington, KY
United States