Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles
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Data
2009-01-01
Autores
Gonçalves, Daciberg Lima
Penteado, Dirceu
Vieira, João Peres [UNESP]
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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. © 2009 Juliusz Schauder Center for Nonlinear Studies.
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Abelianized obstruction, Fiber bundle, Fiberwise homotopy, Fixed point
Como citar
Topological Methods in Nonlinear Analysis, v. 33, n. 2, p. 293-305, 2009.