Twisted conjugacy classes in nilpotent groups

By Daciberg Lima Gonçalves, Peter Wong. 2007

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Abstract A group is said to have the R ∞ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R ∞ 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 ∞ property. The R ∞ property for virtually abelian and for -nilpotent groups are also discussed.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/08e90e4411470af8c0783b83baabbd47d9a6b7a0