WHAT IS...an Acylindrical Group Action?

WHAT IS ... an acylindrical group action?

The group Z acts on the real line R by translation. It is difficult to find a nontrivial group action which is easier to understand: the orbit of every point moves off to infinity at a steady and predictable rate, and the group action preserves the usual Euclidean metric on R. Of course, this action is a covering space action, and the quotient space of the action is the circle, which is complet...

iSAN - An Intelligent Storage Area Network Architecture

This paper describes the motivation, architecture and implementation of iSAN, an “intelligent” storage area network. The main contributions of this work are: (1) how to architect an intelligent SAN that understands the storageconsumers to serve them better; (2) how to realise this abstract architecture using existing technologies; and (3) to demonstrate the benefits that would accrue from such ...

Strike action - what then?

Boundary C∗-algebras for Acylindrical Groups

Let ∆ be an infinite, locally finite tree with more than two ends. Let Γ < Aut(∆) be an acylindrical uniform lattice. Then the boundary algebra AΓ = C(∂∆) Γ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.

Acylindrical accessibility for groups acting on R-trees

We prove an acylindrical accessibility theorem for finitely generated groups acting on R-trees. Namely, we show that if G is a freely indecomposable non-cyclic k-generated group acting minimally and M-acylindrically on an R-tree X then for any ǫ > 0 there is a finite subtree Yǫ ⊆ X of measure at most 2M (k − 1) + ǫ such that GYǫ = X. This generalizes theorems of Z.Sela and T.Delzant about actio...