| Private Homepage | https://ivv5hpp.uni-muenster.de/u/bartelsa/ |
| Project membership Mathematics Münster | B: Spaces and Operators B2: Topology |
| Current Publications | • Bartels A, Bestvina M The Farrell-Jones conjecture for mapping class groups. Inventiones Mathematicae Vol. 215 (2), 2019, pp 651-712 online • Bartels A, Douglas CL, Henriques A Fusion of defects. Memoirs of the American Mathematical Society Vol. 258 (1237), 2019, pp vii+100 online • Bartels A, Douglas CL, Henriques A Conformal nets IV: The 3-category. Algebraic and Geometric Topology Vol. 18 (2), 2018, pp 897-956 online |
| Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - C03: K-theory of group algebras We will study K-theory of group algebras via assembly maps. A key tool is the Farrell—Jones Conjecture for group rings and its extension to Hecke algebra. We will study in particular integral Hecke algebras, investigate Efimov’s continuous K-theory as an alternative to controlled algebra in the context of the Farrell-Jones conjecture, and study vanishing phenomena for high dimensional cohomology of arithmetic groups. • 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 | bartelsa at math dot uni-muenster dot de |
| Phone | +49 251 83-33745 |
| FAX | +49 251 83-32774 |
| Room | 512 |
| Secretary | Sekretariat AG Topologie Frau Claudia Rüdiger Telefon +49 251 83-35159 Fax +49 251 83-38370 Zimmer 516 Sekretariat SFB 1442 Telefon +49 251 83- Fax +49 251 83- Zimmer Sekretariat des Sonderforschungsbereichs 1442 |
| Address | Prof. Dr. Arthur Bartels Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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