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On equivariant deformation of maps
Vidal, Antonio

Data: 1988
Resum: 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 flA 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 Xis 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(fl (x A» = 0. As a consequence we obtain a special case of a theorem of Wilczynski (cf . [12, Theorem A] ~. Finally, motivated by Wilczynski's paper we present an interesting question concerning the equivariant version of the converse of the Lefschetz fixed point theorem.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 32 n. 1 (1988) p. 115-121, ISSN 0214-1493

Adreça alternativa:
DOI: 10.5565/PUBLMAT_32188_10
DOI: 10.5565/37550

7 p, 217.1 KB

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