caa a22 4500 445884193 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9530-7 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9530-7 A relationship between twisted conjugacy classes and the geometric invariants Ω n [Elektronische Daten] [Nic Koban, Peter Wong] A group G is said to have the property R ∞ if every automorphism $${\varphi \in {\rm Aut}(G)}$$ has an infinite number of φ-twisted conjugacy classes. Recent work of Gonçalves and Kochloukova uses the Σn (Bieri-Neumann-Strebel-Renz) invariants to show the R ∞ property for a certain class of groups, including the generalized Thompson's groups F n,0. In this paper, we make use of the Ωn invariants, analogous to Σn, to show R ∞ for certain finitely generated groups. In particular, we give an alternate and simpler proof of the R ∞ property for BS(1, n). Moreover, we give examples for which the Ωn invariants can be used to determine the R ∞ property while the Σn invariants techniques cannot. Springer Science+Business Media B.V., 2010 Twisted conjugacy class nationallicence Property R ∞ nationallicence Σ-invariants nationallicence Ω-invariants nationallicence Koban Nic Department of Mathematics, University of Maine Farmington, 04938, Farmington, ME, USA aut Wong Peter Department of Mathematics, Bates College, 04240, Lewiston, ME, USA aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 233-243 0046-5755 151:1<233 2011 151 10711 https://doi.org/10.1007/s10711-010-9530-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9530-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Koban Nic Department of Mathematics, University of Maine Farmington, 04938, Farmington, ME, USA aut NATIONALLICENCE 700 1- Wong Peter Department of Mathematics, Bates College, 04240, Lewiston, ME, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 233-243 0046-5755 151:1<233 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer