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Fakultät für Mathematik Universität Regensburg
The index theorem by Atiyah and Singer, Part II
Semester
SoSe 2017

Lecturer
Bernd Ammann, Karsten Bohlen

Type of course (Veranstaltungsart)
Vorlesung

Contents
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.

Literature
see webpage of the winter term and summer term

Recommended previous knowledge
Atiyah-Singer index theorem in the Chern-Weil formalism.

Time/Date
Friday 8:30-10.00

Location
M009

Course homepage
http://www.mathematik.uni-regensburg.de/ammann/lehre/2016w_index/index2.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Oral examination (without grade): Duration: 30 minutes, Date: individually arranged
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes, Date: individually arranged, re-exam: Date: individually
    arranged
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Pruefungsleistung; die Note ergibt sich aus der Pruefungsleistung
  • Unbenotet:
    • O. g. Studienleistung
Modules
BV, MV, MGAGeo

ECTS
3
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