Description

• Title:
  Motion planning in polyhedral products of groups and a Fadell-Husseini approach to topological complexity
• Creator:
  Aguilar-Guzmán, Jorge Aguilar-Guzmán;
  González, Jesús
• Description:
  We compute the topological complexity of a polyhedral product $\mathcal{Z}$ defined {in terms of} an $\operatorname{LS}$-logarithmic family of locally compact connected $\operatorname{CW}$ topological groups. The answer is given by a combinatorial formula that involves the $\operatorname{LS}$ category of the polyhedral-product factors. As a by-product, we show that the Iwase-Sakai conjecture holds true for $\mathcal{Z}$. The proof methodology {uses} a Fadell-Husseini viewpoint for the monoidal topological complexity $\big(\mathsf{TC}^M\big)$ of a space, which, under mild conditions, recovers Iwase-Sakai's original definition. In the Fadell-Husseini context, the stasis condition - $\mathsf{TC}^M$'s \emph{raison d'\^etre} - can be encoded at the covering level. Our Fadell-Husseini inspired definition provides an alternative to the $\mathsf{TC}^M$ variant given by Dranishnikov, as well as to the ones provided by Garc\'ia-Calcines, Carrasquel-Vera and Vandembroucq in terms of relative category.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Jorge Aguilar-Guzmán Aguilar-Guzmán, Jesús González;
  https://creativecommons.org/licenses/by-nd/4.0
• 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); 37 - 57;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42813/34968 ;https://apcz.umk.pl/TMNA/article/view/42813/34969
• Subject:
  Monoidal topological complexity;
  Iwase-Sakai conjecture;
  Fadell-Husseini topological complexity;
  polyhedral product;
  relative category;
  55M30, 55M15, 68T40
• Identifier: https://apcz.umk.pl/TMNA/article/view/42813
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other