Lück, Wolfgang

[["dc.bibliographiccitation.firstpage","518"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Geometric and Functional Analysis"],["dc.bibliographiccitation.lastpage","567"],["dc.bibliographiccitation.volume","9"],["dc.contributor.author","Lück, W."],["dc.contributor.author","Schick, T."],["dc.date.accessioned","2017-09-07T11:47:16Z"],["dc.date.available","2017-09-07T11:47:16Z"],["dc.date.issued","1999"],["dc.description.abstract","Suppose M¯ is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological torsion of M¯ and the L2-analytic torsion of the Riemannian manifold M are equal. In particular, the L2-topological torsion of M¯ is proportional to the hyperbolic volume of M, with a constant of proportionality which depends only on the dimension and which is known to be nonzero in odd dimensions [HS]. In dimension 3 this proves the conjecture [Lü2, Conjecture 2.3] or [LLü, Conjecture 7.7] which gives a complete calculation of the L2-topological torsion of compact L2-acyclic 3-manifolds which admit a geometric JSJT-decomposition.¶In an appendix we give a counterexample to an extension of the Cheeger-Müller theorem to manifolds with boundary: if the metric is not a product near the boundary, in general analytic and topological torsion are not equal, even if the Euler characteristic of the boundary vanishes."],["dc.identifier.doi","10.1007/s000390050095"],["dc.identifier.gro","3146701"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4494"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1016-443X"],["dc.title","L2-torsion of Hyperbolic Manifolds of Finite Volume"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","31"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Forum Mathematicum"],["dc.bibliographiccitation.lastpage","65"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Lück, Wolfgang"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2017-09-07T11:47:11Z"],["dc.date.available","2017-09-07T11:47:11Z"],["dc.date.issued","2005"],["dc.identifier.doi","10.1515/form.2005.17.1.31"],["dc.identifier.gro","3146680"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4471"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0933-7741"],["dc.title","Approximating ^2ehBsignatures by their compact analogues"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","362"],["dc.bibliographiccitation.lastpage","399"],["dc.contributor.author","Lück, Wolfgang"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.editor","Farrell, F. T."],["dc.contributor.editor","Lück, Wolfgang"],["dc.date.accessioned","2017-09-07T11:47:14Z"],["dc.date.available","2017-09-07T11:47:14Z"],["dc.date.issued","2003"],["dc.description.abstract","For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the -version of the Baum-Connes conjecture imply the L2-signature theorem for a normal covering over a Poincaré space, provided that the group of deck transformations is torsion-free. We discuss the various possible definitions of L2-signatures (using the signature operator, using the cap product of differential forms, using a cap product in cellular L2-cohomology, …) in this situation, and prove that they all coincide."],["dc.identifier.doi","10.1142/9789812704443_0015"],["dc.identifier.gro","3146683"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4474"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","World Scientific Publishing"],["dc.publisher.place","River Edge"],["dc.relation.conference","ICTP 2001"],["dc.relation.eventend","2001-06-08"],["dc.relation.eventlocation","Italien"],["dc.relation.eventstart","2001-05-21"],["dc.relation.isbn","978-981-238-223-8"],["dc.relation.ispartof","High-Dimensional Manifold Topology"],["dc.title","Various ^2ehBsignatures and a topological ^2ehBsignature theorem"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","315"],["dc.bibliographiccitation.lastpage","321"],["dc.contributor.author","Linnell, Peter A."],["dc.contributor.author","Lück, Wolfgang"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.editor","Farrell, F. T."],["dc.contributor.editor","Lück, Wolfgang"],["dc.date.accessioned","2017-09-07T11:47:14Z"],["dc.date.available","2017-09-07T11:47:14Z"],["dc.date.issued","2003"],["dc.description.abstract","Let G = ℤ/2ℤ ≀ ℤ be the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka notebook problem. Assume that kG is contained in a ring R in which the element 1 – x is invertible, with x a generator of ℤ ⊂ G. Then R is not flat over kG. If k = ℂ, this applies in particular to the algebra of unbounded operators affiliated to the group von Neumann algebra of G. We present two proofs of these results. The second one is due to Warren Dicks, who, having seen our argument, found a much simpler and more elementary proof, which at the same time yielded a more general result than we had originally proved. Nevertheless, we present both proofs here, in the hope that the original arguments might be of use in some other context not yet known to us."],["dc.identifier.doi","10.1142/9789812704443_0013"],["dc.identifier.gro","3146684"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4475"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","World Scientific Publishing"],["dc.relation.conference","ICTP 2001"],["dc.relation.eventend","2001-06-08"],["dc.relation.eventlocation","Trieste"],["dc.relation.eventstart","2001-05-21"],["dc.relation.isbn","978-981-238-223-8"],["dc.relation.ispartof","High-Dimensional Manifold Topology"],["dc.subject","Ore ring affiliated operators flat lamplighter group Fox calculus"],["dc.title","The Ore condition, affiliated operators, and the lamplighter group"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

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