|
Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Dirac operators in coarse geometry SemesterWiSe 2026 / 27 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Vorlesung German title Diracoperatoren und grobe Geometrie Contents Coarse geometry is the framework to study large scale geometry. Some interesting spectral properties of Dirac operators on complete manifolds, in particular the essential spectrum, are invariant under local changes. So it is natural to study them using methods of coarse geometry. In this course we give an introduction to coarse geometry in general, and coarse K-homology as an example of a coarse homology. We then consider Dirac-type operators on complete manifolds and capture their index classes in coarse K-homology. We apply these ideas to index theory and geometry, e.g. by finding obstructions against positive scalar curvature. This course is for advanced master students and PhD-students with a modest background in global analysis or Riemannian geometry. Literature This course is intended as an introduction to the field using the language as developed in https://arxiv.org/pdf/1607.03657. More concretely we will explain parts of https://arxiv.org/pdf/1706.06959 and https://arxiv.org/pdf/2411.01646. Time/Date Fr 12-14 Location M103 Registration
MV, MGAGeo ECTS 3 |