Lecture Series on Transgression and Flows, March 1-10, 2016

Dienstag, 1.3., 10am

Title: Transgressions and flows. An overview.

Abstract: Using certain types of Morse-Smale flows on compact manifolds one can produce concrete instances of Poincare Duality, best understood in the context of currents. We will give a panoramic view of how that works, including some classical examples such as the Chern-Gauss-Bonnet Theorem. 

Donnerstag, 3.3., 10am

Title: Construction of the Bott-Samelson resolution with corners

Abstract: One fundamental ingredient for producing transgression formulas in the sense of currents using flows is a finite volume theorem for unstable manifolds of Morse-Smale flows. We will look at the details of the construction of a manifold with corners resolution from which this kind of theorem follows immediately.

Dienstag, 8.3., 10am

Title: Examples of transgression formulas

Abstract: The plan is to present with a fair amount of details two relatively new applications of the theory: an odd version of Chern-Gauss-Bonnet and Quillen's Chern character currents associated to superconnections.

Mittwoch, 9.3., 10am

Title: Smooth cohomology and sparks

Abstract: We will give an overview of Harvey-Lawson-Zweck theory of sparks that produces groups which are naturally isomorphic with the classical differential characters groups (smooth cohomology) of Cheeger and Simons. We will analyze an example of such a spark bearing the name of Maslov.

Donnerstag, 10.3., 10am

Title: Transgressions on manifolds with boundary

Abstract: We will talk about Lefschetz Duality in the context of currents and explain how the celebrated Chern-Gauss-Bonnet for manifolds with boundary fits in this ambient. Moreover we describe how Thom isomorphism can be contemplated in this picture.