Description

• Title:
  The $R_{\infty}$ property for infra-nilmanifolds
• Creator:
  Dekimpe, Karel;
  de Rock, Bram;
  Penninckx, Pieter
• Description:
  In this paper, we investigate the finiteness of the Reidemeister number $R(f)$ of a selfmap $f\colon M\to M$ on an infra-nilmanifold $M$. We show that the Reidemeister number of an Anosov diffeomorphism on an infra-nilmanifold is always finite. A manifold $M$ is said to have the $R_\infty$ property if $R(f)=\infty$ for every homeomorphism $f\colon M\to M$. We show that every non-orientable generalised Hantzsche-Wendt manifold has the $R_\infty$ property. For an orientable Hantzsche-Wendt manifold $M$, we formulate a criterion, in terms of an associated graph, for $M$ to have the $R_\infty$ property.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 34, No 2 (December 2009); 353 - 373;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.047/8637
• Subject:
  Reidemeister number;
  infra-nilmanifolds;
  Hantzsche-Wendt manifolds;
  Primary 55M20;
  Secondary 20F34
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.047
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other