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.