Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1773-1848 |
| Number of pages | 76 |
| Journal | Geometry and Topology |
| Volume | 26 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 Mathematical Sciences Publishers.
Funding
Barthel was partly supported by the DNRF92 and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement 751794. Stapleton was supported by NSF grant DMS-1906236.
| Funders | Funder number |
|---|---|
| National Science Foundation (NSF) | DMS-1906236 |
| Horizon 2020 Framework Programme | |
| H2020 Marie Skłodowska-Curie Actions | 751794 |
Keywords
- Stolz–Teichner program
- elliptic cohomology
- equivariant K-theory
- power operations
- supersymmetric field theories
ASJC Scopus subject areas
- Geometry and Topology