Braiding Self-Equivalences with Bordism (Kürsat Sözer)

Orateur : Kürsat Sözer

Lieu : salle des Séminaires M3

Résumé :

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.