 
Summary: TOPOLOGICAL HOCHSCHILD HOMOLOGY OF CONNECTIVE
COMPLEX KTHEORY
By CHRISTIAN AUSONI
Abstract. Let ku be the connective complex Ktheory 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 Smodules 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 Salgebra 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
