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Journal of the London Mathematical Society 2000 62(2):345-356; doi:10.1112/S0024610700008929
© 2000 by London Mathematical Society
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© The London Mathematical Society

Topological Hochschild Homology

R. Schwänzl, R. M. Vogt and F. Waldhausen

Fachbereich Mathematik/Informatik, Universität Osnabrück D-49069 Osnabrück, Germany
Fakultät für Mathematik, Universität Bielefeld Postfach 100131, D-33501 Bielefeld, Germany

Received 18 December 1998. Revision received 1 June 1999.

In the appendix to [20] Waldhausen discussed a trace map tr:K(R)->HH(R), from the algebraic K-theory of a ring to its Hochschild homology, which can be used to obtain information about K(R) from HH(R). In [1] Bökstedt described a factorization of this trace map. The intermediate functor THH(HR) is called the topological Hochschild homology of the Eilenberg–MacLane spectrum HR associated with R, because it is constructed similarly to Hochschild homology with the tensor product replaced by the smash product of spectra.


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