1,721,026 research outputs found
Sofic groups and diophantine approximation
No full textWe prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic. (c) 2007 Wiley Periodicals, Inc
L-2-cohomology for von Neumann algebras
No full textWe study L-2-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [CoS]. We give a definition of L-2-cohomology and show how the study of the first L-2-Betti number can be related to the study of derivations with values in a bi-module of affiliated operators. We show several results about the possibility of extending derivations from sub-algebras and about uniqueness of such extensions. In particular, we show that the first L-2-Betti number of a tracial von Neumann algebra coincides with the corresponding number for an arbitrary weakly dense sub-C -algebra. Along the way, we prove some results about the dimension function of modules over rings of affiliated operators which are of independent interest
L-2-BETTI NUMBERS FOR SUBFACTORS
No full textWe study L-2-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [2], in the presence of a bi-finite correspondence, and prove a proportionality formula
L-2-BETTI NUMBERS FOR SUBFACTORS
No full textWe study L-2-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [2], in the presence of a bi-finite correspondence, and prove a proportionality formula
On a conjecture of Gottlieb
No full textWe give a counterexample to a conjecture of D H Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW–complex X to an aspherical CW–complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation all components of non-zero degree maps in the space of maps from X to Y are contractible. We use L 2 –Betti numbers and homological algebra over von Neumann algebras to prove the modified conjecture
Short laws for finite groups and residual finiteness growth
Full text link We prove that for every n ∈ N n \in \mathbb {N} and δ > 0 \delta >0 there exists a word w n ∈ F 2 w_n \in F_2 of length O ( n 2 / 3 log ( n ) 3 + δ ) O(n^{2/3} \log (n)^{3+\delta }) which is a law for every finite group of order at most n n . This improves upon the main result of Andreas Thom [Israel J. Math. 219 (2017), pp. 469–478] by the second named author. As an application we prove a new lower bound on the residual finiteness growth of non-abelian free groups. </p
A spectral sequence to compute L²-Betti numbers of groups and groupoids
Full text linkWe construct a spectral sequence for L-2-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More generally, we obtain a permanence result for the Hopf-Singer conjecture under taking fiber bundles whose base space is an aspherical manifold with poly-surface fundamental group. As further sample applications of the spectral sequence, we obtain new vanishing theorems and explicit computations of L-2-Betti numbers of groups and manifolds and obstructions to the existence of normal subrelations in measured equivalence relations.DFG [SA 1661/1-1]; Max-Planck-Institute in Bon
Homology of free quantum groups
Full text linkWe compute the Hochschild homology of the free orthogonal quantum group A(0)(n). We show that it satisfies Poincare duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive results about the l(2)-homology of A(0)(n) and estimates on the free entropy dimension of its set of generators. In particular, we show that the l(2) Betti-numbers of A(0)(n) all vanish and that the free entropy dimension is less than 1. To cite this article: B. Collins et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights, reserved.NSERC; ANR; JSPS; DFG [534, 1493]; CR
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
