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Rope solo experiment

Well, the weather has been too good not to go climbing, so I headed down to Donation yesterday afternoon.  Much to my surprise, I had the whole place to myself.

The picture (not very good) shows the rope solo system that I used.  This is my first time using the Peztl MiniTraxion for this purpose. (One advantage of having climbed a couple of walls is that one has a lot of interesting gear to play with on an occasion like this.)

Rope solo system picture

Rope solo system

Steph Davis has a good post on rope solo systems (and the follow-up comments are helpful too).  What I did was tie the climbing rope in to the anchor at its midpoint, with a figure-8 knot on a steel biner, so I had two independent anchored strands.  One strand went through the mini-traxion, which rode on a full strength chest harness (also clipped to the sit-harness by a short sling).  The other strand went through a Gri-Gri.

When climbing, the mini-traxion side was weighted to my gear bag and then fed automatically.  the Gri-Gri side I pulled rope through when convenient, and also tied off with a separate backup knot every now and again.   To transition to rappel, just open the cam on the mini-trax and rappel on the Gri-Gri.

At first I was pretty nervous trusting the system and moved very slowly and inelegantly.  But it soon became clear that it would work fine.  The pulley moves up with you and gives a good catch.   Still, I should probably have started with something a bit easier.  Things feel different when you are the only one around!

If working something steep, one should carry prusiks so as to be able to unweight the mini-trax and transition to rappel when hanging in space.  Of course, one could bring ascenders; but that seems to be taking the idea of raiding the aid box to an unnecessary extreme!

 

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

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

The lower central series and pseudo-Anosov dilatations

Authors:
Benson 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
entropy dimension $leq 1$

Authors:
Kenley 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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