Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Topological Hochschild homology of K/p as a Kp module

Pages: 253 – 280

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a13

Author

Samik Basu (Department of Mathematics, Vivekananda University, Belur, Howrah, West Bengal, India)

Abstract

For commutative ring spectra R, one can construct a Thom spectrum for spaces over BGL1R. This specialises to the classical Thom spectra for spherical fibrations in the case of the sphere spectrum. The construction is useful in detecting A-structures: a loop space (up to homotopy) over BGL1R yields an A-ring structure on the Thom spectrum. The topological Hochschild homology of these A-ring spectra may be expressed as Thom spectra.

This paper uses the identification of topological Hochschild homology of Thom spectra to make computations. Specifically, we take R to be the p-adic K-theory spectrum and consider a certain map from S1 to BGL1R, so that the Thom spectrum is equivalent to the modp K-theory spectrum. We make computations at odd primes.

Keywords

Thom spectra, topological Hochschild homology, K-theory

2010 Mathematics Subject Classification

Primary 55P42. Secondary 55N15, 55P43.

Published 6 June 2017