Results 1  10
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43
Hilbert modules and modules over finite von Neumann algebras and applications to L²invariants
 MATH. ANN. 309, 247285 (1997)
, 1997
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The relation between the BaumConnes conjecture and the trace conjecture
 Invent. Math
"... We prove a version of the L 2index Theorem of Atiyah, which uses the universal centervalued trace instead of the standard trace. We construct for Gequivariant Khomology an equivariant Chern character, which is an isomorphism and lives over the ring Z ⊂ Λ G ⊂ Q obtained from the integers by inver ..."
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Cited by 14 (10 self)
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We prove a version of the L 2index Theorem of Atiyah, which uses the universal centervalued trace instead of the standard trace. We construct for Gequivariant Khomology an equivariant Chern character, which is an isomorphism and lives over the ring Z ⊂ Λ G ⊂ Q obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the BaumConnes Conjecture implies the modified Trace Conjecture, which says that the image of the standard trace K0(C ∗ r (G)) → R takes values in Λ G. The original Trace Conjecture predicted that its image lies in the additive subgroup of R generated by the inverses of all the orders of the finite subgroups of G, and has been disproved by Roy [13].
ON THE DIFFERENTIAL FORM SPECTRUM OF HYPERBOLIC MANIFOLDS
, 2003
"... Abstract. We give a lower bound for the bottom of the L 2 differential form spectrum on hyperbolic manifolds, generalizing thus a wellknown result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodgede Rham Laplacian and lea ..."
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Cited by 8 (1 self)
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Abstract. We give a lower bound for the bottom of the L 2 differential form spectrum on hyperbolic manifolds, generalizing thus a wellknown result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodgede Rham Laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds. 1.
L 2 −cohomology of manifolds with flat ends
 Geom. Funct. Anal. 13 n
"... We give a topological interpretation of the space of L 2harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a ChernGaussBonnet formula for the L 2Euler characteristic of some of these Manifolds. These results are applications of general theor ..."
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Cited by 8 (1 self)
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We give a topological interpretation of the space of L 2harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a ChernGaussBonnet formula for the L 2Euler characteristic of some of these Manifolds. These results are applications of general theorems on complete Riemannian Manifold whose GaussBonnet operator is nonparabolic at infinity. Résumé: Nous donnons une interprétation topologique des espaces de formes harmoniques L 2 d’une variété riemannienne complète plate l’infini. Ceci répond une question posée par J. Dodziuk. Nous obtenons aussi une formule de ChernGaussBonnet pour la caractéristique d’Euler L 2 de certaines de ces variétés. Ces résultats sont des conséquences de théorèmes généraux sur les variétés riemanniennes complètes dont l’opérateur de GaussBonnet est nonparabolique l’infini.
Nearcohomology Of Hilbert Complexes And Topology Of Nonsimply Connected Manifolds.
, 1992
"... this paper we follow the abstract setting from [5] and give a rened formulation of the abstract result there. This leads to a new notion of near{cohomology for Hilbert complexes. We take a special family of quadric cones depending on a small positive parameter and consisting of cochains which have c ..."
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Cited by 7 (0 self)
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this paper we follow the abstract setting from [5] and give a rened formulation of the abstract result there. This leads to a new notion of near{cohomology for Hilbert complexes. We take a special family of quadric cones depending on a small positive parameter and consisting of cochains which have coboundaries which are small with respect to the distance of the cochains to the space of all cocycles. Heuristically this means that we take cochains with small coboundaries modulo cochains close to cocycles. (Instead of cochains close to cocycles we could also take cochains close to coboundaries which would remind cohomology Typeset by A
Singular traces, dimensions, and NovikovShubin invariants
 Proceedings of the 17th OT Conference, Theta
, 2000
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Noncommutative Riemann integration and NovikovShubin invariants for Open Manifolds
, 2001
"... Given a C ∗algebra A with a semicontinuous semifinite trace τ acting on the Hilbert space H, we define the family A R of bounded Riemann measurable elements w.r.t. τ as a suitable closure, à la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions [2 ..."
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Cited by 6 (3 self)
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Given a C ∗algebra A with a semicontinuous semifinite trace τ acting on the Hilbert space H, we define the family A R of bounded Riemann measurable elements w.r.t. τ as a suitable closure, à la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions [26], and show that A R is a C ∗algebra, and τ extends to a semicontinuous semifinite trace on A R. Then, unbounded Riemann measurable operators are defined as the closed operators on H which are affiliated to A ′′ and can be approximated in measure by operators in A R, in analogy with unbounded Riemann integration. Unbounded Riemann measurable operators form a τa.e. bimodule on A R, denoted by A R, and such bimodule contains the functional calculi of selfadjoint elements of A R under unbounded Riemann measurable functions. Besides, τ extends to a bimodule trace on A R.
Residual amenability and the approximation of L 2 –invariants
 Michigan Math. J
, 1999
"... Abstract. We generalize Lück’s Theorem to show that the L 2Betti numbers of a residually amenable covering space are the limit of the L 2Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant cla ..."
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Cited by 6 (0 self)
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Abstract. We generalize Lück’s Theorem to show that the L 2Betti numbers of a residually amenable covering space are the limit of the L 2Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L 2 torsion is a homotopy invariant for such spaces. We give examples of residually amenable groups, including the BaumslagSolitar groups.