Units of ring spectra and their traces in algebraicK–theory
Copyright policy )Units of ring spectra and their traces in algebraicK–theory
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)->��^{\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 ��_{i-1}(R) not annihilated by the stable Hopf map give rise to non-trivial classes in K_i(R) for i\geq 3.
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.html
- University of Oslo Norway
ring spectra, algebraic K-theory, Algebraic \(K\)-theory of spaces, 19D55, 19D10, Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.), topological Hochschild homology, Loop space machines and operads in algebraic topology, VDP::410, 55P43, FOS: Mathematics, Algebraic Topology (math.AT), 55P48, algebraic K theory, 19D55, 55P43, 19D10, 55P48, \(K\)-theory and homology; cyclic homology and cohomology, Mathematics - Algebraic Topology
ring spectra, algebraic K-theory, Algebraic \(K\)-theory of spaces, 19D55, 19D10, Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.), topological Hochschild homology, Loop space machines and operads in algebraic topology, VDP::410, 55P43, FOS: Mathematics, Algebraic Topology (math.AT), 55P48, algebraic K theory, 19D55, 55P43, 19D10, 55P48, \(K\)-theory and homology; cyclic homology and cohomology, Mathematics - Algebraic Topology
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