Description

• Title:
  Nielsen coincidence theory of fibre-preserving maps and Dold's fixed point index
• Creator:
  Gonçalves, Daciberg L.;
  Koschorke, Ulrich
• Description:
  Let $M \to B$, $N \to B$ be fibrations and $f_1,f_2\colon M \to N$ be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair $f_1$, $f_2$ over $B$ to a coincidence free pair of maps. In the special case where the two fibrations are the same and one of the maps is the identity, a weak version of our $\omega$-invariant turns out to equal Dold's fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over $B$ are developed. As an illustration we compute e.g the minimal number of coincidence components for all homotopy classes of maps between $S^1$-bundles over $S^1$ as well as their Nielsen and Reidemeister numbers.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 1 (March 2009); 85 - 103;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.007/8646
• Subject:
  Coincidence;
  fixed point;
  map over B;
  normal bordism;
  $\omega$-invariant;
  Nielsen number;
  Reidemeister class;
  Dold's index;
  fibration;
  Primary 55M20;
  Secondary 55R05;
  55S35;
  57R19;
  57R90
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.007
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other