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KL2MG-interactions SIGNED

K-theory, L^2-invariants, manifolds, groups and their interactions

Total Cost €

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EC-Contrib. €

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Partnership

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 KL2MG-interactions project word cloud

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Project "KL2MG-interactions" data sheet

The following table provides information about the project.

Coordinator
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN 

Organization address
address: REGINA PACIS WEG 3
city: BONN
postcode: 53113
website: www.uni-bonn.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 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

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN DE (BONN) coordinator 1˙719˙583.00

Map

 Project objective

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.

 Publications

year authors and title journal last update
List of publications.
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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