Volume 8, issue 2 (2004)

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Units of ring spectra and their traces in algebraic $K$–theory

Christian Schlichtkrull

Geometry & Topology 8 (2004) 645–673

arXiv: math.AT/0405079

Abstract

Let GL1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition

ηR: BGL1(R) K(R) THH(R) Ω(R),

where K(R) is the algebraic K–theory and THH(R) the topological Hochschild homology of R. As a corollary we show that classes in πi1R not annihilated by the stable Hopf map η π1s(S0) give rise to non-trivial classes in Ki(R) for i 3.

Keywords
ring spectra, algebraic K-theory, topological Hochschild homology
Mathematical Subject Classification 2000
Primary: 19D55, 55P43
Secondary: 19D10, 55P48
References
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Publication
Received: 25 November 2003
Revised: 21 April 2004
Accepted: 13 March 2004
Published: 22 April 2004
Proposed: Thomas Goodwillie
Seconded: Ralph Cohen, Haynes Miller
Authors
Christian Schlichtkrull
Department of Mathematics
Oslo University
PO Box 1053
Blindern
NO-0316 Oslo
Norway