Private Homepagehttps://ivv5hpp.uni-muenster.de/u/bartelsa/
Selected PublicationsBartels, A. Coarse flow spaces for relatively hyperbolic groups. Compositio Mathematica Vol. 153 (4), 2017, pp 745-779 online
Bartels, A.; Farrell, F.T.; Lück, W. The Farrell-Jones conjecture for cocompact lattices in virtually connected Lie groups. Journal of the American Mathematical Society Vol. 27 (2), 2014, pp 339-388 online
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, C.L.; Henriques, A. Fusion of defects. Memoirs of the American Mathematical Society Vol. 258, 2019, pp vii+100 online
Bartels, A.; Douglas, C.L.; Henriques; A. Conformal nets V: Dualizability. Communications in Mathematical Physics Vol. 391 (1), 2022 online
Bartels A, Douglas CL, Henriques A Conformal nets II: Conformal blocks. Communications in Mathematical Physics Vol. 354 (1), 2017, pp 393-458 online
Bartels, A.; Lück, W. The Borel Conjecture for hyperbolic and CAT(0)-groups. Annals of Mathematics Vol. 175 (2), 2012, pp 631-689 online
Bartels, A.; Lück, W.; Reich, H. The K-theoretic Farrell-Jones conjecture for hyperbolic groups. Inventiones Mathematicae Vol. 172 (1), 2008 online
Bartels, A.; Lück, W.; Weinberger, S. On hyperbolic groups with spheres as boundary. Journal of Differential Geometry Vol. 86 (1), 2010, pp 1-16 online
Bartels, A.; Reich, H. On the Farrell-Jones conjecture for higher algebraic K-theory. Journal of the American Mathematical Society Vol. 18 (3), 2005, pp 501--545 (electronic) online
Topics in
Mathematics Münster


T1: K-Groups and cohomology
T2: Moduli spaces in arithmetic and geometry
Current PublicationsBartels, A.; Douglas, C.L.; Henriques; A. Conformal nets V: Dualizability. Communications in Mathematical Physics Vol. 391 (1), 2022 online
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, C.L.; Henriques, A. Fusion of defects. Memoirs of the American Mathematical Society Vol. 258, 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 ProjectsCRC 1442 - 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.

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
E-Mailbartelsa at math dot uni-muenster dot de
Phone+49 251 83-33745
FAX+49 251 83-32774
Room512
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
AddressProf. Dr. Arthur Bartels
Mathematisches Institut
Fachbereich Mathematik und Informatik der Universität Münster
Einsteinstrasse 62
48149 Münster
Deutschland
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