You currently have no access to view or download this content. Please log in with your institutional or personal account if you should have access to this content through either of these.
Showing a limited preview of this publication:
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.
Received: 2007-06-26
Revised: 2008-03-04
Published Online: 2009-06-16
Published in Print: 2009-August
© Walter de Gruyter Berlin · New York 2009