| Private Homepage | http://wwwmath.uni-muenster.de/u/jeber_02/johannesebert.html |
| Project membership Mathematics Münster | B: Spaces and Operators B2: Topology |
| Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - B03: Moduli spaces of metrics of positive curvature In this project, the space of Riemannian metrics of positive scalar curvature on closed manifolds will be studied. Central research questions concern the nontriviality of secondary index invariants, rigidity theorems for the homotopy type of those spaces and the action of the diffeomorphism group, and the comparison of two iterated loop space structures. We will use techniques from differential geometry, higher index theory, metric geometry, differential topology and homotopy theory. online • CRC 1442: Geometry: Deformation and Rigidity - C01: Automorphisms and embeddings of manifolds This project concerns the homotopical properties of spaces of smooth and topological automorphisms of manifolds, their classifying spaces and spaces of smooth and topological embeddings of manifolds. Known characteristic classes for manifold bundles will play an important role. It is conceivable that new ones will be constructed. The action of automorphisms and embeddings on finite subsets of manifolds, more precisely on the configuration category of a manifold, will be exploited. online • EXC 2044 - B2: Topology We will analyse geometric structures from a topological point of view. In particular, we will study manifolds, their diffeomorphisms and embeddings, and positive scalar curvature metrics on them. Via surgery theory and index theory many of the resulting questions are related to topological K-theory of group C*-algebras and to algebraic K-theory and L-theory of group rings. Index theory provides a map from the space of positive scalar curvature metrics to the K-theory of the reduced C*-algebra of the fundamental group. We will develop new tools such as parameterised coarse index theory and combine them with cobordism categories and parameterised surgery theory to study this map. In particular, we aim at rationally realising all K-theory classes by families of positive scalar curvature metrics. Important topics and tools are the isomorphism conjectures of Farrell-Jones and Baum-Connes about the structure of the K-groups that appear. We will extend the scope of these conjectures as well as the available techniques, for example from geometric group theory and controlled topology. We are interested in the K-theory of Hecke algebras of reductive p-adic Lie groups and in the topological K-theory of rapid decay completions of complex group rings. Via dimension conditions and index theory techniques we will exploit connections to operator algebras and coarse geometry. Via assembly maps in algebraic K- and L-theory we will develop index-theoretic tools to understand tangential structures of manifolds. We will use these tools to analyse the smooth structure space of manifolds and study diffeomorphism groups. Configuration categories will be used to study spaces of embeddings of manifolds. online | johannes dot ebert at uni-muenster dot de |
| Phone | +49 251 83-33092 |
| FAX | +49 251 83-38370 |
| Room | 506 |
| Secretary | Sekretariat AG Topologie Frau Claudia Rüdiger Telefon +49 251 83-35159 Fax +49 251 83-38370 Zimmer 516 |
| Address | Prof. Dr. Johannes Ebert Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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