On equivariant topological modular forms

David Gepner; Lennart Meier

doi:10.1112/S0010437X23007509

On equivariant topological modular forms

David Gepner
, Lennart Meier

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Following ideas of Lurie, we give a general construction of equivariant elliptic cohomology without restriction to characteristic zero. Specializing to the universal elliptic curve we obtain, in particular, equivariant spectra of topological modular forms. We compute the fixed points of these spectra for the circle group and more generally for tori.

Original language	English
Pages (from-to)	2638-2693
Number of pages	56
Journal	Compositio Mathematica
Volume	159
Issue number	12
DOIs	https://doi.org/10.1112/S0010437X23007509
Publication status	Published - 1 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s).

Funding

Despite lacking firm foundations until more recently, equivariant elliptic cohomology is by now an old and diverse subject, going back to the 1980s and admitting applications across much of modern mathematics and physics. Many people have contributed to the subject and their contributions are too numerous to name. However, we would like to thank Matthew Ando, John Greenlees, and Jacob Lurie in particular for shaping our thinking about equivariant elliptic cohomology. We furthermore thank Thomas Nikolaus for his input at the beginning of this project, Viktoriya Ozornova and Daniel Schäppi for useful conversations about categorical questions, and Bastiaan Cnossen and Stefan Schwede for providing references. We thank Bastiaan Cnossen and Sil Linskens for catching a mistake about orbispaces. We thank the referee for their careful reading and insightful comments. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme ‘Homotopy harnessing higher structures’ when work on this paper was undertaken. This work was supported by EPSRC grant number EP/R014604/1. The authors would like to thank the Mathematical Sciences Research Institute for providing an inspiring working environment during the program ‘Higher categories and categorification’. Lastly, we want to thank the Hausdorff Research Institute for Mathematics in Bonn for their excellent working conditions.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/R014604/1

Keywords

elliptic cohomology
equivariant homotopy theory
orbispaces
topological modular forms

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On equivariant topological modular forms

Abstract

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Keywords

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