Description

• Title:
  The Borsuk-Ulam property for cyclic groups
• Creator:
  Izydorek, Marek;
  Marzantowicz, Wacław
• Description:
  An orthogonal representation $V$ of a group $G$ is said to have the Borsuk-Ulam property if the existence of an equivariant map $f:S(W) \rightarrow S(V)$ from a sphere of representation $W$ into a sphere of representation $V$ implies that $\dim W \leq \dim V$. It is known that a sufficient condition for $V$ to have the Borsuk-Ulam property is the nontriviality of its Euler class ${\text {\bf e}}(V)\in H^{*} (BG;\mathcal R)$. Our purpose is to show that ${\text {\bf e}}(V) \neq 0 $ is also necessary if $G$ is a cyclic group of odd and double odd order. For a finite group $G$ with periodic cohomology an estimate for $G$-category of a $G$-space $X$ is also derived.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2000.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 16, No 1 (September 2000); 65 - 72;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.030/9975
• Subject:
  Equivariant maps;
  the Euler class;
  G-category;
  Primary;
  57S17;
  55M30;
  Secondary;
  55R25;
  55S35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2000.030
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other