Units of ring spectra and their traces in algebraic K-theory
Algebraic Topology
2014-11-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0405079,
title = {Units of ring spectra and their traces in algebraic K-theory},
author = {Christian Schlichtkrull},
journal= {arXiv preprint arXiv:math/0405079},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.html