Induced quasi-actions: A remark

Induced Quasi-actions: a Remark

If the permutation action ρI is transitive, all factors Xi are quasiisometric to each other, and the restricted quasi-actions Gi y Xi are quasi-conjugate (when identifying different stabilizers Gi by inner automorphisms of G). The main result of this note is that in this case any of the quasi-actions Gi y Xi determines ρ up to quasi-conjugacy, and moreover any quasi-conjugacy class may arise as...

A Remark on Quasi-isometries

We show that if f : Bn -IRn is an e-quasi-isometry, with e < 1, defined on the unit ball Bn of Rn, then there is an affine isometry h : Bn -Rn with lIf(x) -h(x)|I < Ce(l+logn) where C is a universal constant. This result is sharp.

A Remark about Dihedral Group Actions on Spheres

We show that a finite dihedral group does not act pseudofreely and locally linearly on an even-dimensional sphere S, with k > 1. This answers a question of R. S. Kulkarni from 1982.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Quasi-actions on trees I. Bounded valence

Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T ′. This theorem has many applications: quasi-isometric rigidity for fundamental groups of finite, bushy graphs of coarse PD(n) groups for each fixed n; a generalization to actions on Cantor sets of Sullivan’s theorem abou...