Summary: TOPOLOGICAL HOCHSCHILD HOMOLOGY OF CONNECTIVE
By CHRISTIAN AUSONI
Abstract. Let ku be the connective complex K-theory spectrum, completed at an odd prime p. We
present a computation of the mod (p, v1) homotopy algebra of the topological Hochschild homology
spectrum of ku.
1. Introduction. Since the discovery of categories of spectra with a sym-
metric monoidal smash product, as for instance the S-modules of [EKMM], the
topological Hochschild homology spectrum THH(A) of a structured ring spec-
trum A can be defined by translating the definition of Hochschild homology of
an algebra into topology, using a now standard "Algebra Brave New Algebra"
dictionary. The algebraic origin of this definition sheds light on many features
of topological Hochschild homology, and has also led to more conceptual proofs
of results that were based on B¨okstedt's original definition [B¨o1] of topological
Hochschild homology for functors with smash products, see for instance [SVW2].
As can be expected by analogy with the algebraic situation, this definition also
highlights the role that topological Hochschild (co-)homology plays in the clas-
sification of S-algebra extensions. See for example [SVW1], [La] or [BJ] for
applications to extensions.
The aim of this paper is to exploit the advantages of such an algebraic def-