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Odd primary analogs of real orientations

Jeremy Hahn, Andrew Senger and Dylan Wilson

Geometry & Topology 27 (2023) 87–129
Abstract

We define, in Cp–equivariant homotopy theory for p > 2, a notion of μp–orientation analogous to a C2–equivariant Real orientation. The definition hinges on a Cp–space μp, which we prove to be homologically even, in a sense generalizing recent C2–equivariant work on conjugation spaces.

We prove that the height p 1 Morava E–theory is μp–oriented and that tmf (2) is μ3–oriented. We explain how a single equivariant map v1μp: S2ρ Σμ p completely generates the homotopy of Ep1 and tmf (2), expressing a height-shifting phenomenon pervasive in equivariant chromatic homotopy theory.

Keywords
chromatic homotopy theory, equivariant
Mathematical Subject Classification
Primary: 55P43, 55P91, 55P92
References
Publication
Received: 21 October 2020
Revised: 28 July 2021
Accepted: 6 September 2021
Published: 1 May 2023
Proposed: Stefan Schwede
Seconded: Mark Behrens, Jesper Grodal
Authors
Jeremy Hahn
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Andrew Senger
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Dylan Wilson
Department of Mathematics
Harvard University
Cambridge, MA
United States

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