Description

• Title:
  The size of some critical sets by means of dimension and algebraic $\varphi$-category
• Creator:
  Pintea, Cornel
• Description:
  Let $M^n$, $N^n$, $n\geq 2$, be compact connected manifolds. We first observe that mappings of zero degree have high dimensional critical sets and show that the only possible degree is zero for maps $f\colon M\to N$, under the assumption on the index $[\pi_1(N):{\rm Im}(f_*)]$ to be infinite. By contrast with the described situation one shows, after some estimates on the algebraic $\varphi$-category of some pairs of finite groups, that a critical set of smaller dimension keeps the degree away from zero.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 2 (June 2010); 395 - 407;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.023/8468
• Subject:
  Critical points/values;
  degree of maps;
  algebraic $\varphi$-category;
  Primary 58K05;
  Secondary 57R70
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other