03.07.2025, 16:15
– Raum 1.22
Forschungsseminar Differentialgeometrie
Heat and resolvent expansions in the noncommutative case
Matthias Lesch (Bonn)
We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary.
Using Cheeger-Chern-Simons characters, we introduce the notion of differential trivializations of universal characteristic classes. Specializing to the class ½ p1 ∈ H4(BSpinn, Z) this yields a notion of differential String classes. Differential String classes turn out to be stable isomorphism classes of geometric String structures.