Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

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Data

2009-06-01

Autores

Goncalves, Daciberg Lima
Penteado, Dirceu
Vieira, João Peres [UNESP]

Título da Revista

ISSN da Revista

Título de Volume

Editor

Juliusz Schauder Ctr Nonlinear Studies

Resumo

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Descrição

Palavras-chave

Fixed point, fiber bundle, fiberwise homotopy, abelianized obstruction

Como citar

Topological Methods In Nonlinear Analysis. Torun: Juliusz Schauder Ctr Nonlinear Studies, v. 33, n. 2, p. 293-305, 2009.