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Units of ring spectra and their traces in algebraic K-theory

Christian Schlichtkrull

Published 2004-05-05Version 1

Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->\Omega^{\infty}(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 \pi_{i-1}(R) not annihilated by the stable Hopf map give rise to non-trivial classes in K_i(R) for i\geq 3.

Comments: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.html
Journal: Geom. Topol. 8(2004) 645-673
Categories: math.AT
Subjects: 19D55, 55P43, 19D10, 55P48
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