Description

• Title:
  Abelianized Obstruction for fixed points of fiber-preserving maps of Surface bundles
• Creator:
  Gonçalves, Daciberg L.;
  Penteado, Dirceu;
  Vieira, João Peres
• Description:
  Let $f\colon M \to M$ be a fiber-preserving map where $S\to M \to B$ is a bundle and $S$ is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform $f$ to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 2 (June 2009); 293 - 305;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.019/8609
• Subject:
  Fixed point;
  fiber bundle;
  fiberwise homotopy;
  abelianized obstruction;
  Primary 55M20;
  Secondary 55R10;
  55S35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.019
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other