Description

• Title:
  Symmetric topological complexity for finite spaces and classifying spaces
• Creator:
  Tanaka, Kohei
• Description:
  We present a combinatorial approach to the symmetric motion planning in polyhedra using finite spaces. For a finite space $P$ and a positive integer $k$, we introduce two types of combinatorial invariants, $\mathrm{CC}^{S}_k(P)$ and $\mathrm{CC}^{\Sigma}_k(P)$, that are closely related to the design of symmetric robotic motions in the $k$-iterated barycentric subdivision of the associated simplicial complex $\mathcal{K}(P)$. For the geometric realization $\mathcal{B}(P)=|\mathcal{K}(P)|$, we show that the first $\mathrm{CC}^{S}_k(P)$ converges to Farber-Grant's symmetric topological complexity $\mathrm{TC}^{S}(\mathcal{B}(P))$ and the second $\mathrm{CC}^{\Sigma}_k(P)$ converges to Basabe-Gonz\'alez-Rudyak-Tamaki's symmetrized topological complexity $\mathrm{TC}^{\Sigma}(\mathcal{B}(P))$ as $k$ becomes larger.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.27
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2 (December 2019); 477 - 493;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.048/18045 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.048/18046
• Subject:
  Finite space;
  symmetric topological complexity;
  configuration space;
  order complex;
  classifying space;
  Primary;
  55P10;
  Secondary;
  06A07;
  55U35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.048
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other