Twisted conjugacy classes in nilpotent groups

Author(s)

Goncalves, Daciberg ^[1] ; Wong, Peter ^[2]

Affiliation

^[1] Univ Sao Paulo, IME, Dept Matemat, BR-05311970 Sao Paulo - Brazil

^[2] Bates Coll, Dept Math, Lewiston, ME 04240 - USA

• Document type: Journal article
• Source: JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK; v. 633, p. 11-27, AUG 2009.
• Web of Science Citations: 24

Abstract

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed. (AU)

• FAPESP's process: 00/05385-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants