Applications of the Atiyah and Singer index theorem

Prof. Bernd Ammann, Zimmer 119, and Karsten Bohlen

Content of the lecture

This 2-hour lecture continues the lecture from last semester. In the winter term we have proved the Atiyah-Singer theorem using the heat kernel method. In the summer term we will consider applications of the theorem. We will discuss the Gauss-Bonnet-Chern theorem, consequences in the Kähler case, and other facts associated to spin geometry potentially reaching to recent research projects. If time admits, we will also discuss several generalisations, e.g.: The index theorem for elliptic operators of arbitrary order by using the "reduction to Dirac" by Baum and Douglas. The L2-index theorem. Enlargeability obstruction to positive scalar curvature. KO-valued index and obstructions in dim 1 and 2 mod 8. The family index theorem and applications to the topology of the space of metrics with positive scalar curvature. The positive mass theorem of general relativity for spin manifolds.

Recommeded previous knowledge

Atiyah-Singer index theorem in the Chern-Weil formalism.



Lecture notes (Diverse Vorlesungsskripte)

Place and Time

Friday, 8-10, M009

Recommended Links

Related web sites

Bernd Ammann, 29.11.2016 oder später