[math/0606120] Maximal rank maps between Riemannian manifolds with bounded geometry

This paper by Abreu-Suzuki gives a condition under which a coarse submersion between Riemannian manifolds is coarsely a product.

Interesting not only in itself but for its references - which are to another author (Kumeu) who came up with the basic coarse ideas, in the context of bg Riemannian manifolds, in the middle 1980s. I had not been aware of this before.

## Wednesday, June 07, 2006

## Sunday, April 23, 2006

### GT Monographs: Volume 9

GT Monographs: Volume 9

This is the proceedings of an Oberwolfach conference on "exotic" homology manifolds. (Roughly speaking, these are manifolds for which the "zero'th Pontrjagin class" is not equal to 1.)

This is the proceedings of an Oberwolfach conference on "exotic" homology manifolds. (Roughly speaking, these are manifolds for which the "zero'th Pontrjagin class" is not equal to 1.)

## Thursday, March 30, 2006

### [math/0603675] The lower central series and pseudo-Anosov dilatations

[math/0603675] The lower central series and pseudo-Anosov dilatations

Authors:

Comments: 26 pages, 6 figures

Subj-class: Geometric Topology; Dynamical Systems

MSC-class: 37E30 (Primary) 57M60, 37B40 (Secondary)

## The lower central series and pseudo-Anosov dilatations

Authors:

Benson Farb,

Christopher J. Leininger,

Dan MargalitBenson Farb,

Christopher J. Leininger,

Dan Margalit

Comments: 26 pages, 6 figures

Subj-class: Geometric Topology; Dynamical Systems

MSC-class: 37E30 (Primary) 57M60, 37B40 (Secondary)

The theme of this paper is that algebraic complexity implies dynamical

complexity for pseudo-Anosov homeomorphisms of a closed surface S_g of genus g.

Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov

homeomorphism of S_g tends to zero at the rate 1/g. We consider here the

smallest dilatation of any pseudo-Anosov homeomorphism of S_g acting trivially

on Gamma/Gamma_k, the quotient of Gamma = pi_1(S_g) by the k-th term of its

lower central series, k > 0. In contrast to Penner's asymptotics, we prove that

this minimal dilatation is bounded above and below, independently of g, with

bounds tending to infinity with k. For example, in the case of the Torelli

group I(S_g), we prove that L(I(S_g)), the logarithm of the minimal dilatation

in I(S_g), satisfies .197 < L(I(S_g))< 4.127. In contrast, we find

pseudo-Anosov mapping classes acting trivially on Gamma/Gamma_k whose

asymptotic translation lengths on the complex of curves tend to 0 as g tends

toward infinity.

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### [math/0603669] All generating sets of all property T von Neumann algebras have free entropy dimension $\leq 1$

[math/0603669] All generating sets of all property T von Neumann algebras have free entropy dimension $\leq 1$

## All generating sets of all property T von Neumann algebras have free

Authors:

Comments: 6 pages

Subj-class: Operator Algebras

MSC-class: 46L54; 52C17

## All generating sets of all property T von Neumann algebras have free

entropy dimension $\leq 1$

Authors:

Kenley Jung,

Dimitri ShlyakhtenkoKenley Jung,

Dimitri Shlyakhtenko

Comments: 6 pages

Subj-class: Operator Algebras

MSC-class: 46L54; 52C17

Suppose $N$ is a diffuse, property T von Neumann algebra and X is an

arbitrary finite generating set of selfadjoint elements for N. By using

rigidity/deformation arguments applied to representations of N in full matrix

algebras, we deduce that the microstate spaces of X are asymptotically discrete

up to unitary conjugacy. We use this description to show that the free entropy

dimension of X, $\delta_0(X)$, is less than or equal to 1. It follows that when

N embeds into the ultraproduct of the hyperfinite $\mathrm{II}_1$-factor, then

$\delta_0(X)=1$ and otherwise, $\delta_0(X)=-\infinity$. This generalizes the

earlier results of Voiculescu, and Ge, Shen pertaining to $SL_n(\mathbb Z)$ as

well as the results of Connes, Shlyakhtenko pertaining to group generators of

arbitrary property T algebras.

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Which authors of this paper are endorsers?

## Tuesday, March 28, 2006

### [math/0603621] Property A, partial translation structures and uniform embeddings in groups

[math/0603621] Property A, partial translation structures and uniform embeddings in groups

Brodzki, Niblo, Wright. - I blogged this before, but now there is an explicit invariant.

Brodzki, Niblo, Wright. - I blogged this before, but now there is an explicit invariant.

## Friday, March 03, 2006

### Interesting Mathematics

Interesting Mathematics

Here is a paper by Ursula Hamenstadt proving exactness of the mapping class group. The method is interesting and is related to ideas of Kaimanovich. It is math.GR/0510116. One can look on her web page for other papers as well. http://www.math.uni-bonn.de/people/ursula/papers.html

Here is a paper by Ursula Hamenstadt proving exactness of the mapping class group. The method is interesting and is related to ideas of Kaimanovich. It is math.GR/0510116. One can look on her web page for other papers as well. http://www.math.uni-bonn.de/people/ursula/papers.html

## Thursday, March 02, 2006

### [math/0603018] On the space of metrics with invertible Dirac operator

[math/0603018] On the space of metrics with invertible Dirac operator

This paper by Mattias Dahl shows that several geometric constructions, eg codim-3 surgery, which one knows how to do in the category of positive scalar curvature manifolds, can in fact be done in the category of spin manifolds with invertible Dirac operator.

This paper by Mattias Dahl shows that several geometric constructions, eg codim-3 surgery, which one knows how to do in the category of positive scalar curvature manifolds, can in fact be done in the category of spin manifolds with invertible Dirac operator.

## Tuesday, January 31, 2006

### [math/0601700] Representations of residually finite groups by isometries of the Urysohn space

[math/0601700] Representations of residually finite groups by isometries of the Urysohn space: "Representations of residually finite groups by isometries of the Urysohn space

Authors: Vladimir G. Pestov, Vladimir V. Uspenskij

Comments: 12 pages, LaTeX 2e

Subj-class: Representation Theory

MSC-class: 43A65; 20C99; 22A05; 22F05; 22F50; 54E50

As a consequence of Kirchberg's work, Connes Embedding Conjecture is equivalent to the property that every homomorphism of the group $F_\infty\times F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is pointwise approximated by homomorphisms with a precompact range. In this form, the property (which we call Kirchberg's property) makes sense for an arbitrary topological group. We establish the validity of the Kirchberg property for the isometry group $Iso(U)$ of the universal Urysohn metric space $U$ as a consequence of a stronger result: every representation of a residually finite group by isometries of $U$ can be pointwise approximated by representations with a finite range. This brings up the natural question of which other concrete infinite-dimensional groups satisfy the Kirchberg property."

Authors: Vladimir G. Pestov, Vladimir V. Uspenskij

Comments: 12 pages, LaTeX 2e

Subj-class: Representation Theory

MSC-class: 43A65; 20C99; 22A05; 22F05; 22F50; 54E50

As a consequence of Kirchberg's work, Connes Embedding Conjecture is equivalent to the property that every homomorphism of the group $F_\infty\times F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is pointwise approximated by homomorphisms with a precompact range. In this form, the property (which we call Kirchberg's property) makes sense for an arbitrary topological group. We establish the validity of the Kirchberg property for the isometry group $Iso(U)$ of the universal Urysohn metric space $U$ as a consequence of a stronger result: every representation of a residually finite group by isometries of $U$ can be pointwise approximated by representations with a finite range. This brings up the natural question of which other concrete infinite-dimensional groups satisfy the Kirchberg property."

## Thursday, January 26, 2006

### [math/0512592] Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity

[math/0512592] Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity

Here's an interesting paper from the arXiv by Behrstock, Drutu and Mosher

Here's an interesting paper from the arXiv by Behrstock, Drutu and Mosher

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