Algebraic Topology Seminar
Andrew Blumberg
UT Austin
The algebraic K-theory of the sphere spectrum
Abstract: Waldhausen showed that the algebraic K-theory of the “spherical group
ring” on the based loops of a manifold captures the stable concordance
space of the manifold. In the simplest case, this result says that for
high-dimensional disks, information about BDiff is encoded in K(S), the
algebraic K-theory of the sphere spectrum. This talk explains recent work
with Mike Mandell that provides a complete calculation of the homotopy
groups of K(S) in terms of the homotopy groups of K(Z), the sphere
spectrum, and a certain Thom spectrum. I will also explain what we know
about the homotopy type of K(S) in terms of a kind of K-theoretic
Tate-Poitou duality.
Monday March 30, 2015 at 3:00 PM in SEO 1227