Description

• Title:
  Classical Morse theory revisited - I backward $\lambda$-lemma and homotopy type
• Creator:
  Weber, Joa
• Description:
  We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs $(N,L)$, established in \cite{weber:2014c}, as a \emph{dynamical thickening of the stable manifold}. As a first application and to illustrate efficiency of the concept we reprove a fundamental theorem of classical Morse theory, Milnor's homotopical cell attachment theorem \cite{milnor:1963a}. Dynamical thickening leads to a conceptually simple and short proof.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 2 (June 2016); 641 - 646;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.020/8013 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.020/8014
• Subject:
  Morse theory;
  homotopy type;
  flow selector;
  37Dxx;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.020
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other