Description

• Title:
  The Borsuk-Ulam property for homotopy classes of maps from the torus to the Klein bottle
• Creator:
  Gonçalves, Daciberg Lima;
  Guaschi, John;
  Laass, Vinicius Casteluber
• Description:
  Let $M$ be a topological space that admits a free involution $\tau$, and let $N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to have {\it the Borsuk-Ulam property with respect to $\tau$} if for every representative map $f\colon M \to N$ of $\beta$, there exists a point $x \in M$ such that $f(\tau(x))= f(x)$. In this paper, we determine the homotopy classes of maps from the $2$-torus $\mathbb{T}^2$ to the Klein bottle $\mathbb{K}^2$ that possess the Borsuk-Ulam property with respect to a free involution $\tau_1$ of $\mathbb{T}^2$ for which the orbit space is $\mathbb{T}^2$. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of $\mathbb{T}^2$ and $\mathbb{K}^2$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.12.18
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 2 (December 2020); 529 - 558;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.003/27446 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.003/27447
• Subject:
  Borsuk-Ulam theorem;
  homotopy class;
  braid groups;
  surfaces;
  Primary;
  55M20;
  57M07;
  Secondary;
  20F36
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.003
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other