Abelianized Obstruction for fixed points of fiber-preserving maps of Surface bundles
Keywords
Fixed point, fiber bundle, fiberwise homotopy, abelianized obstructionAbstract
Let $f\colon M \to M$ be a fiber-preserving map where $S\to M \to B$ 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.Downloads
Published
2009-06-01
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GONÇALVES, Daciberg L., PENTEADO, Dirceu and VIEIRA, João Peres. Abelianized Obstruction for fixed points of fiber-preserving maps of Surface bundles. Topological Methods in Nonlinear Analysis. Online. 1 June 2009. Vol. 33, no. 2, pp. 293 - 305. [Accessed 28 March 2024].
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