Homology, Homotopy and Applications
Volume 19 (2017)
Number 1
Topological Hochschild homology of as a 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 , one can construct a Thom spectrum for spaces over . This specialises to the classical Thom spectra for spherical fibrations in the case of the sphere spectrum. The construction is useful in detecting -structures: a loop space (up to homotopy) over yields an -ring structure on the Thom spectrum. The topological Hochschild homology of these -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 to be the -adic -theory spectrum and consider a certain map from to , so that the Thom spectrum is equivalent to the -theory spectrum. We make computations at odd primes.
Keywords
Thom spectra, topological Hochschild homology, -theory
2010 Mathematics Subject Classification
Primary 55P42. Secondary 55N15, 55P43.
Published 6 June 2017