Groups of Piecewise Linear Homeomorphisms

Abstract

Abstract. In this paper we study a class of groups which may be described as groups of piecewise linear bijections of a circle or of compact intervals of the real line. We use the action of these groups on simplicial complexes to obtain homological and combinatorial information about them. We also identify large simple subgroups in all of them, providing examples of finitely presented infinite simple groups.

Thompson’s group is distorted in the Thompson–Stein groups

“…, n k ) Standard presentations. Stein [1992] gave a method for finding the finite presentations for the groups F(n 1 , . .…”

“…Theorem 3.1 [Stein 1992;Wladis 2009]. Thompson's group F(2, 3) admits the infinite presentation with generators x 0 , y 0 , z 0 , x 1 , y 1 , z 1 , .…”

“…. , n k ), generalizing F, were first explored in depth by Melanie Stein [1992]. Related explorations of general classes in this family of groups, each of which can be considered to be a generalization of the Thompson groups, include [Higman 1974;Brown and Geoghegan 1984;Brown 1987;Brin and Guzmán 1998;Brin and Squier 2001;Bieri and Strebel 1985].…”

“…, n k in each linear piece. We abbreviate F(2) by F. Stein [1992] explored the homological and simplicity properties of F(n 1 , . .…”

Кусочно-гладкие гомеoморфизмы окружности с несколькими изломами

“…[12]). Инвариантные меры КЛ гомеоморфизмов окружности с двумя изломами впервые изучались в работе [13].…”