| Private Homepage | https://ivv5hpp.uni-muenster.de/u/bartelsa/ |
| Selected Publications | • Bartels, 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 Publications | • Bartels, 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 Projects | • EXC 2044 - T01: K-Groups and cohomology K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to geometric topology to operator algebras. The idea is to associate algebraic invariants to geometric objects, for example to schemes or stacks, C∗-algebras, stable ∞-categories or topological spaces. Originating as tools to differentiate topological spaces, these groups have since been generalized to address complex questions in different areas. online • EXC 2044 - T02: Moduli spaces in arithmetic and geometry The term “moduli space” was coined by Riemann for the space Mg parametrizing all one-dimensional complex manifolds of genus g. Variants of this appear in several mathematical disciplines. In arithmetic geometry, Shimura varieties or moduli spaces of shtukas play an important role in the realisation of Langlands correspondences. Diffeomorphism groups of high-dimensional manifolds and moduli spaces of manifolds and of metrics of positive scalar curvature are studied in differential topology. Moduli spaces are also one of the central topics in our research in mathematical physics, where we study moduli spaces of stable curves and of Strebel differentials. online • CRC 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. | bartelsa at math dot uni-muenster dot de |
| Phone | +49 251 83-33745 |
| FAX | +49 251 83-38370 |
| 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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