The Segal conjecture for topological Hochschild homology of complex cobordism

Details The Segal conjecture for topological Hochschild homology of complex cobordism The Segal conjecture for topological Hochschild homology of complex cobordism

2010-10-27

arxiv.org/abs/1010.5635v2

Mathematics

Algebraic Topology

Accepted for publication by the Journal of Topology

Scientific paper

We study the C_p-equivariant Tate construction on the topological Hochschild homology THH(B) of a symmetric ring spectrum B by relating it to a topological version R_+(B) of the Singer construction, extended by a natural circle action. This enables us to prove that the fixed and homotopy fixed point spectra of THH(B) are p-adically equivalent for B = MU and BP. This generalizes the classical C_p-equivariant Segal conjecture, which corresponds to the case B = S.

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