On equivariant deformations of maps.

Vidal, Antonio

Publicacions Matemàtiques, Tome 32 (1988), p. 115-121 / Harvested from Biblioteca Digital de Matemáticas

Résumé

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.

Détail

Publié le : 1988-01-01

MR MR0939775 | Zbl 0649.57003

DMLE-ID : 3589