SIGMA THEORY AND TWISTED CONJUGACY, II: HOUGHTON GROUPS AND PURE SYMMETRIC AUTOMORPHISM GROUPS

Autor(es)

Goncalves, Daciberg L. ^[1] ; Sankaran, Parameswaran ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Math, Caixa Postal 66281, BR-05314970 Sao Paulo, SP - Brazil

^[2] Inst Math Sci, CIT Campus, Madras 600113, Tamil Nadu - India

• Tipo de documento: Artigo Científico
• Fonte: PACIFIC JOURNAL OF MATHEMATICS; v. 280, n. 2, p. 349-369, FEB 2016.
• Citações Web of Science: 4

Resumo

Let phi : Gamma -> Gamma be an automorphism of a group Gamma. We say that x, y is an element of Gamma are in the same phi-twisted conjugacy class and write x similar to(phi) y if there exists an element gamma is an element of Gamma such that y = gamma x phi(gamma(-1)). This is an equivalence relation on Gamma called the phi-twisted conjugacy. Let R(phi) denote the number of phi-twisted conjugacy classes in Gamma. If R(phi) is infinite for all phi is an element of Aut(Gamma), we say that Gamma has the R-infinity-property. The purpose of this note is to show that the symmetric group S-infinity, the Houghton groups and the pure symmetric automorphism groups have the R-infinity-property. We show, also, that the Richard Thompson group T has the R-infinity-property. We obtain a general result establishing the R-infinity-property of the finite direct product of finitely generated groups. This is a sequel to an earlier work by Gonalves and Kochloukova, in which it was shown using the sigma theory of Bieri, Neumann and Strebel that, for most of the groups Gamma considered here, R(phi) = infinity where phi varies in a finite index subgroup of the automorphisms of Gamma. (AU)

• Processo FAPESP: 12/24454-8 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático