Tuesday 23 September 2025, 16:00 - 17:00 in HG00.310
Murat Saglam (Cologne)
On contact mapping classes of prequantization spaces
The main objects of this talk are prequantization spaces, i.e. principal circle bundles over closed manifolds such that the curvature form is an integral symplectic form. Our focus is to understand the geometry of the natural contact structure on such spaces, namely the horizontal distribution defined by a connection 1-form. We will see that for a suitably chosen base symplectic manifold, the contact geometry of the associated prequantization space is very rich in the following sense: there are infinitely many diffeomorphisms of such prequantization spaces that are smoothly isotopic to the identity but mutually non-isotopic as diffeomorphisms preserving the contact structure. Our proofs are based on classical algebraic topological methods.