On equivariant deformations of maps.

Título inglés On equivariant deformations of maps.
Título español Sobre la deformación equivariante de aplicaciones.
Autor/es Vidal, Antonio
Organización Inst. Estud. Catalanes, Barcelona, España
Revista 0214-1493
Publicación 1988, 32 (1): 115-121, 12 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 121003
Palabras clave español Grupos de transformación ; Deformación equivariante ; Número de Lefschetz
Código MathReviews MR0939775
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