Parametrized homotopy theory and bivariant A-theory

Monday 29 Feb 2016, 14:00 → 16:00 Europe/Brussels

E/1st floor-E.161 - Meeting room (E.161) (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

George Raptis (U. Regensburg) Waldhausen's algebraic K-theory of spaces is an extension of algebraic K-theory from rings to spaces or ring spectra, which encodes the stable homotopy type as well as important geometric information of the space. Bivariant A-theory, introduced by B. Williams, is a further extension of algebraic K-theory from spaces to fibrations of spaces. In this talk, I will recall the definition and basic properties of bivariant A-theory and discuss its connection with parametrized homotopy theory. Time permitting, I will also explain how bivariant A-theory enters in the study of the A-theory Euler characteristic and the Dwyer-Weiss-Williams theorems. (Parts of this talk are based on separate joint works with John Lind, and with Wolfgang Steimle.)