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Power operations in the
Stolz–Teichner program
Tobias Barthel, Daniel Berwick-Evans and Nathaniel Stapleton |
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Geometry & Topology 26 (2022) 1773–1848
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Abstract |
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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. |
Keywords
elliptic cohomology, supersymmetric field theories,
equivariant K-theory, power operations, Stolz–Teichner
program
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Mathematical Subject Classification
Primary: 55N34, 81T60, 55S25
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References |
Publication
Received: 2 July 2020
Revised: 26 May 2021
Accepted: 27 June 2021
Published: 28 October 2022
Proposed: Mark Behrens
Seconded: Marc Levine, Stefan Schwede
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Authors |
| Tobias Barthel | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Daniel Berwick-Evans | |
| Department of Mathematics University of Illinois at Urbana–Champaign Urbana, IL United States |
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| Nathaniel Stapleton | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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