Pontryagin classes of topological bundles

Søren Galatius, University of Copenhagen

Online Talk

Pontryagin classes of real vector bundles are usually defined as Chern classes of the complexified bundle. In rational cohomology they can be defined more generally for euclidean bundles -- fiber bundles with fiber R^n and structure group the entire homeomorphism group of R^n. The question of whether familiar relations, such as p_n = e^2 for 2n-dimensional vector bundles, hold for euclidean bundles has recently been answered in the negative by Weiss. My talk will discuss joint work (arXiv:2208.11507) with Randal-Williams on related questions.