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

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

2004-05-05

arxiv.org/abs/math/0405079v1

Geom. Topol. 8(2004) 645-673

Mathematics

Algebraic Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.html

Scientific paper

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.

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