|
Differential Cohomology SemesterSoSe 2024 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Vorlesung German title Differentielle Kohomologie Contents Differential cohomology combines deRham cohomology with a generalized cohomology theory with the aim to capture characteristic classes together with their deRham representatives in a common object. In this course I will give an overview on the field starting with classical constructions (like Chern-Weyl theory, Cheever-Simons classes ...) and ending with the modern homotopy theoretic point of view initiated by the work of Hopkins-Singer. A will show how differential cohomology ideas can be used to construct secondary invariants for manifolds and geometric vector bundles. Further applications are construction of regulators for algebraic K-Theory and the formulation of secondary index theorems. Literature much of the material is contained in <A href="https://arxiv.org/abs/1208.3961">pdf </A> Recommended previous knowledge - language of infinity categories - algebraic topology (generalized homology and cohomology theories) - differential geometry (manifolds, vector bundles, connections and curvature) Time/Date Do 14-16 Location M103 Registration
MV ECTS 3 |