Quasi-effect

Quasi-effects are a term from geometric group theory that generalizes the group-theoretical concept of the effect of a group .

In evidence, quasi-effects are often a more flexible tool than effects.

definition

A quasi-effect of a group on a metric space is a mapping ${\displaystyle (K,C)}$ ${\displaystyle G}$ ${\displaystyle X}$

${\displaystyle A\colon G\times X\to X}$

${\displaystyle (g,x)\to gx:=A(g,x)}$

With

• for each there is one - quasi-isometry , ${\displaystyle g\in G}$ ${\displaystyle A(g,.)\colon X\to X}$ ${\displaystyle (K,C)}$
• for all true ${\displaystyle x\in X,g,h\in G}$

${\displaystyle d(g(hx),(gh)x)\leq C}$.

literature

• L. Mosher, M. Sageev, K. Whyte: Quasi-actions on trees. I. Bounded valence , Ann. of Math. (2) 158, 115-164, 2003.
• J. Manning, N. Monod, B. Rémy: Quasi-actions on trees and property QFA , J. London Math. Sol. (2) 73, 84-108, 2006.