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.
- Lin's theorem
- Segal conjecture
- Topological Hochschild homology
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