Twisted conjugacy in PL-homeomorphism groups of the circle

Author(s)

Goncalves, Daciberg Lima ^[1] ; Sankaran, Parameswaran ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Math IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

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

• Document type: Journal article
• Source: Geometriae Dedicata; v. 202, n. 1, p. 311-320, OCT 2019.
• Web of Science Citations: 0

Abstract

Given an automorphism phi : Gamma -> Gamma of a group, one has a left action of Gamma on itself defined as g.x = gx phi(g(-1)). The orbits of this action are called the Reidemeister classes or phi-twisted conjugacy classes. We denote by R(phi) is an element of N boolean OR [infinity] the Reidemeister number of phi, namely, the cardinality of the orbit space R(phi) if it is finite and R(phi) = infinity if R(phi) is infinite. The group Gamma is said to have the R-infinity-property if R(phi) = infinity for all automorphisms phi is an element of Aut(Gamma). We show that the generalized Thompson group T (r, A, P) has the R-infinity-property when the slope group P subset of R->0(x) is not cyclic. (AU)

• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants