Description

• Title:
  Sectional category and the fixed point property
• Creator:
  Zapata, Cesar A. Ipanaque;
  González, Jesús
• Description:
  For a Hausdorff space $X$, we exhibit an unexpected connection between the sectional number of the Fadell-Neuwirth fibration $\pi_{2,1}^X\colon F(X,2)\to X$, and the fixed point property (FPP) for self-maps on $X$. Explicitly, we demonstrate that a space $X$ has the FPP if and only if 2 is the minimal cardinality of open covers $\{U_i\}$ of $X$ such that each $U_i$ admits a continuous local section for $\pi_{2,1}^X$. This characterization connects a standard problem in fixed point theory to current research trends in topological robotics.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.11.27
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 2 (December 2020); 559 - 578;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.033/27126 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.033/27127
• Subject:
  Fixed point property;
  configuration spaces;
  sectional category;
  motion planning problem;
  Primary;
  55M20;
  55R80;
  55M30;
  Secondary;
  68T40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.033
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other