On equivariant deformations of maps

• Autores: Antonio Vidal Estarriol
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 32, Nº 1, 1988, págs. 115-121
• Idioma: inglés
• Títulos paralelos:
  • Sobre la deformación equivariante de aplicaciones
• Enlaces
  • Texto completo
• Resumen

  • We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f|A fixpointfree, where A is a closed invariant submanifold of X with codim A = 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed point free map if and only if the usual Lefschetz number L(f|(X,A)) = 0. As a consequence we obtain a sepcial case of a theorem of Wilczynski (cf. [12, Theorem A]).

    Finally, motivated by Wilczynski's paper we present an interesting question concerning the equivalent version of the converse of the Lefschetz fixed point theorem.