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The index theorem by Atiyah and Singer, Part II SemesterSoSe 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
BV, MV, MGAGeo ECTS 3 |