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Index theory of singular structures SemesterWiSe 2017 / 18 Lecturer Karsten Bohlen Type of course (Veranstaltungsart) Vorlesung Contents The Atiyah-Singer index theorem is a fundamental discovery in the history of mathematics. The theorem states that for any compact manifold without boundary the Fredholm index of elliptic operators is expressed as a topological formula, depending only on the stable homotopy class of the principal symbol of the given operator. This result has numerous deep applications, e.g. to the geometry of Riemannian manifolds and the study of partial differential equations. However mathematical models of physical phenomena are often based on more general structures than the classical smooth manifolds. Using techniques from non-commutative geometry we will study generalizations of the Atiyah-Singer index theory to non-compact manifolds and spaces which have a singular structure. E.g. the orbit spaces of group actions. The index theory of such foliation type structures is strongly connected to versions of the Baum-Connes conjecture. Recommended previous knowledge Differential Geometry Time/Date Mittwoch 14-16 Uhr Location M103 Registration
BV, MV, MGAGeo ECTS 3 |