Date: Oct. 18, 2011

Speaker: John Link, Johns Hopkins University
Title: Higher geometry and algebraic K-theory

Abstract:

A cohomology theory E is particularly useful when we can understand its cocycles E^*(X) in terms of geometric objects associated to the space X.

A basic example is the description of topological K-theory in terms of complex vector bundles. I will give an analogous interpretation of cocycles for E=K(R), the algebraic K-theory of an associative ring spectrum, in terms of bundles of R-modules over X.

The main technical development is a symmetric monoidal model for the category of spaces in which A_{\infty} spaces are strict monoids.