Seminar: Kürşat Sözer - Braiding self-equivalences with bordism (Mar 3, 2026)

Speaker: Kürşat Sözer (Université de Lille)
Title: Braiding self-equivalences with bordism
Time: March 3, 2026 at 19:00 Istanbul local time (17:00 Lille local time)
Place: Online
Meeting ID: 935 6390 4955
Passcode: 699568
Abstract: Spaces of homotopy self-equivalences capture subtle geometric and homotopy-theoretic information about manifolds, but are often difficult to analyze directly. In this talk, I will present a framework that relates these spaces to bordism theories by organizing normal bundle data in a homotopy-theoretic way. For a closed smooth or topological manifold M of dimension at least four, we show that spaces of homotopy self-equivalences preserving prescribed normal information fit into a highly cartesian square involving infinite loop spaces representing certain bordism theories. This leads to braids of interlocking exact sequences connecting homotopy groups of self-equivalence spaces with bordism groups, providing a conceptual generalization of earlier work of Hambleton–Kreck on 4-manifolds. This is joint work with Ian Hambleton and Robin Sroka.