Description

• Title:
  Parametrized topological complexity of sphere bundles
• Creator:
  Farber, Michael;
  Weinberger, Shmuel Weinberger
• Description:
  Parametrized motion planning algorithms \cite{CFW} have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we analyse the parameterized motion planning problem in the case of sphere bundles. Our main results provide upper and lower bounds for the parametrized topological complexity; the upper bounds typically involve sectional categories of the associated fibrations and the lower bounds are given in terms of characteristic classes and their properties. We explicitly compute the parametrized topological complexity in many examples and show that it may assume arbitrarily large values.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Michael Farber, Shmuel Weinberger Weinberger
• Date:
  2023.02.26
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 161 - 177;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42818/34978 ;https://apcz.umk.pl/TMNA/article/view/42818/34979
• Subject:
  Robot motion planning;
  topological complexity;
  motion planning algorithm;
  characteristic classes;
  55M30
• Identifier: https://apcz.umk.pl/TMNA/article/view/42818
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other