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.

Dynamique des échanges d’intervalles des groupes de Higman-Thompson V_{r,m}

“…Définition 1.3 ( [13], voir aussi [4] ou [20]). -On définit le groupe de Higman-Thompson V r,m (resp.…”

Rotation numbers in Thompson–Stein groups and applications

“…Numerous generalisations of Thompson groups have been defined and studied: we recall, for example, the works of Higman [14], Bieri-Strebel [2], Brown [8], Stein [22] and BrinGuzman [6]. In this article, we consider some generalisations of Thompson's groups introduced by Bieri-Strebel and Stein.…”

“…For Thompson-Stein groups M. Stein proved [22] that T r,(n i ) and F r,(n i ) are finitely presented and gave precise homology information.…”

“…(For a proof, see [22,Appendix]). Observe that the definition of (1 − )A implies that this set is a sub-module of A.…”

A simple group generated by involutions interchanging residue classes of the integers

“…Various types of infinite simple groups are treated in the literature so far: we refer to Carter [4] for the simple groups of Lie type, to Higman [9] and Stein [21] for finitely presented simple groups, to Kegel and Wehrfritz [11] for locally finite simple groups, to Baer [1] for composition factors of infinite symmetric groups, and to Ol'shanskii [20] and Chehata [5] for constructions of simple groups with certain given special properties.…”