31.07.25

Manuel Krannich

13:15

Pontryagin classes are certain invariants of vector bundles, which—when applied to tangent bundles—yield invariants of smooth manifolds. These invariants are among the most important invariants of high-dimensional manifolds and have seen numerous applications since their discovery in the 40s, including Milnor’s discovery of exotic spheres. In the 60s, Novikov proved the surprising result that, rationally, these invariants do not depend on the smooth structure of the manifold. In this talk, I will explain an ingenious alternative proof of this result, due to Gromov, which is significantly more elementary than Novikov’s original argument and ultimately relies on the existence of surface bundles over surfaces with nontrivial signature.

SR 3.69