Description

• Title:
  Estimating the discrete Lusternik-Schnirelmann category
• Creator:
  Green, Brian;
  Tsuruga, Mimi;
  Scoville, Nicholas A.
• Description:
  Let $K$ be a simplicial complex and suppose that $K$ collapses onto $L$. Define $n$ to be $1$ less than the minimum number of collapsible sets it takes to cover $L$. Then the discrete geometric Lusternik-Schnirelmann category of $K$ is the smallest $n$ taken over all such $L$. In this paper, we give an algorithm which yields an upper bound for the discrete geometric category. We show our algorithm is correct and give several bounds for the discrete geometric category of well-known simplicial complexes. We show that the discrete geometric category of the dunce cap is $2$, implying that the dunce cap is ``further" from being collapsible than Bing's house whose discrete geometric category is $1$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 45, No 1 (March 2015); 103 - 116;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.006/5341
• Subject:
  Lusternik-Schnirelmann category;
  computational topology;
  collapse;
  simplicial complex;
  Primary 55U10;
  68Q25;
  Secondary 57Q15;
  55M30;
  05E45
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.006
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other