Description

• Title:
  The trivial homotopy class of maps from two-complexes into the real projective plane
• Creator:
  Fenille, Marcio Colombo
• Description:
  We study reasons related to two-dimensional CW-complexes which prevent an extension of the Hopf--Whitney Classification Theorem for maps from those complexes into the real projective plane, even in the simpler situation in which the complex has trivial second integer cohomology group. We conclude that for such a two-complex $K$, the following assertions are equivalent: (1) Every based map from $K$ into the real projective plane is based homotopic to a constant map; (2) The skeleton pair $(K,K^1)$ is homotopy equivalent to that of a model two-complex induced by a balanced group presentation; (3) The number of two-dimensional cells of $K$ is equal to the first Betti number of its one-skeleton; (4) $K$ is acyclic; (5) Every based map from $K$ into the circle $S^1$ is based homotopic to a~constant map.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 603 - 616;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.060/7232 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.060/7233
• Subject:
  Hopf--Whitney Classification Theorem;
  two-dimensional CW complexes;
  group presentation;
  homotopy class;
  cohomology group;
  real projective plane;
  55Q05;
  55Q55
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.060
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other