@article{5298fefb67e242fb924061efc36cbaa3,
title = "Real topological Hochschild homology and the Segal conjecture",
abstract = "We give a new proof, independent of Lin's theorem, of the Segal conjecture for the cyclic group of order two. The key input is a calculation, as a Hopf algebroid, of the Real topological Hochschild homology of F2. This determines the E2-page of the descent spectral sequence for the map NF2→F2, where NF2 is the C2-equivariant Hill–Hopkins–Ravenel norm of F2. The E2-page represents a new upper bound on the RO(C2)-graded homotopy of NF2, from which the Segal conjecture is an immediate corollary.",
keywords = "Equivariant, Lin's theorem, Norm, Segal conjecture, Topological Hochschild homology",
author = "Jeremy Hahn and Dylan Wilson",
note = "Funding Information: We thank Danny Shi and Mingcong Zeng for discussions about their works in progress, and for their patience regarding our hasty and error-prone emails. We thank Hood Chatham for help with some computer calculations we used to explore our E2-page, as well as for his spectral sequence package. We thank J.D. Quigley and Tyler Lawson for sharing their unpublished work on the fixed points (NF2)C2, as well as for providing detailed answers to questions. We thank Mark Behrens for useful discussions, and for sharing a draft of his approach to the Segal conjecture via equivariant homotopy theory. Finally, we thank the anonymous referee for their careful reading and helpful comments. The first author was supported by the NSF under grant DMS-1803273, and the second author under grant DMS-1902669. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = aug,
day = "27",
doi = "10.1016/j.aim.2021.107839",
language = "English (US)",
volume = "387",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}