Explore the words cloud of the KL2MG-interactions project. It provides you a very rough idea of what is the project "KL2MG-interactions" about.
The following table provides information about the project.
Coordinator |
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN
Organization address contact info |
Coordinator Country | Germany [DE] |
Total cost | 1˙719˙583 € |
EC max contribution | 1˙719˙583 € (100%) |
Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
Code Call | ERC-2014-ADG |
Funding Scheme | ERC-ADG |
Starting year | 2015 |
Duration (year-month-day) | from 2015-11-01 to 2020-10-31 |
Take a look of project's partnership.
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1 | RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN | DE (BONN) | coordinator | 1˙719˙583.00 |
Many milestone results in mathematics emerge from interactions and transfer of techniques and methods between different areas. I want to attack outstanding problems concerning K-theory, L^2-invariants, manifolds and group theory. The time is ripe to use the exciting and profound progress that has been made during the last years in the individual areas to build new bridges, gain new insights, open the door to new applications, and to trigger new innovative activities worldwide lasting beyond the proposed funding period.
The starting point are the prominent conjectures of Farrell-Jones on the algebraic K- and L-theory of group rings, of Baum-Connes on the topological K-theory of reduced group C^*-algebras, and of Atiyah on the integrality of L^-Betti numbers.
I intend to analyze and establish the Farrell-Jones Conjecture in other settings such as topological cyclic homology of ``group rings' over the sphere spectrum, algebraic K-theory of Hecke algebras of totally disconnected groups, the topological K-theory of Fr'echet group algebras, and Waldhausen's A-theory of classifying spaces of groups. This has new and far-reaching consequences for automorphism groups of closed aspherical manifolds, the structure of group rings, and representation theory. Recent proofs by the PI of the Farrell-Jones Conjecture for certain classes of groups require input from homotopy theory, geometric group theory, controlled topology and flows on metric spaces, and will be transferred to the new situations. There is also a program towards a proof of the Atiyah Conjecture based on the Farrell-Jones Conjecture and ring theory. Furthermore, I want to attack open problems such as the approximation of L^2-torsion for towers of finite coverings, and the relation of the first L^2-Betti number, the cost and the rank gradient of a finitely generated group. I see a high potential for new striking applications of the Farrell-Jones Conjecture and L^2-techniques to manifolds and groups.
year | authors and title | journal | last update |
---|---|---|---|
2017 |
Markus Land, Thomas Nikolaus, Karol Szumiło Localization of cofibration categories andgroupoid C∗–algebras published pages: 3007-3020, ISSN: 1472-2747, DOI: 10.2140/agt.2017.17.3007 |
Algebraic & Geometric Topology 17/5 | 2019-06-20 |
2018 |
Wolfgang Lück, Peter Linnell Localization, Whitehead groups and the Atiyah conjecture published pages: 33-53, ISSN: 2379-1691, DOI: 10.2140/akt.2018.3.33 |
Annals of K-Theory 3/1 | 2019-06-20 |
2018 |
Land, Markus; Nikolaus, Thomas On the Relation between K- and L-Theory of $C^*$-Algebras published pages: 517-563, ISSN: 0025-5831, DOI: |
Mathematische Annalen volume 371 | 2019-06-20 |
2016 |
Lück, W. and Steimle, W. Splitting the relative assembly map, nil-terms and involutions published pages: 339 - 377, ISSN: 2379-1691, DOI: |
Annals of K-theory vol 1 | 2019-06-20 |
2017 |
Wolfgang Lück, Holger Reich, John Rognes, Marco Varisco Assembly maps for topological cyclic homology of group algebras published pages: , ISSN: 0075-4102, DOI: 10.1515/crelle-2017-0023 |
Journal für die reine und angewandte Mathematik (Crelles Journal) 0/0 | 2019-06-20 |
2015 |
Dubois, J., Friedl, S., and Lück, W. Three flavours of twisted knot invariants published pages: 143-169, ISSN: , DOI: |
Introduction to modern mathematics Adv. Lect. Math. (ALM) 33 | 2019-06-20 |
2017 |
Stefan Friedl, Wolfgang Lück Universal L2-torsion, polytopes and applications to 3-manifolds published pages: 1114-1151, ISSN: 0024-6115, DOI: 10.1112/plms.12035 |
Proceedings of the London Mathematical Society 114/6 | 2019-06-20 |
2020 |
Lueck, Wolfgang Assembly Maps published pages: , ISSN: , DOI: |
to appear in the macbook of homotopy theory 3 | 2019-06-20 |
2019 |
Stefan Friedl, Wolfgang Lück The $L^2$-torsion function and the Thurston norm of 3-manifolds published pages: 21-52, ISSN: 0010-2571, DOI: 10.4171/cmh/453 |
Commentarii Mathematici Helvetici 94/1 | 2019-08-06 |
2018 |
Tom Farrell, Wolfgang Lück, Wolfgang Steimle Approximately fibering a manifold over an aspherical one published pages: 669-726, ISSN: 0025-5831, DOI: |
Mathematische Annalen volume 370 | 2019-06-20 |
2018 |
Nils-Edvin Enkelmann, Wolfgang Lück, Malte Pieper, Mark Ullmann, Christoph Winges On the Farrell–Jones conjecture forWaldhausen’s A–theory published pages: 3321-3394, ISSN: 1465-3060, DOI: 10.2140/gt.2018.22.3321 |
Geometry & Topology 22/6 | 2019-05-10 |
2018 |
Wolfgang Lück Twisting L2-invariants with finite-dimensional representations published pages: 723-816, ISSN: 1793-5253, DOI: 10.1142/S1793525318500279 |
Journal of Topology and Analysis 10/04 | 2019-05-07 |
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