Volume 8, issue 2 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
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
Forward citations
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