Topological Methods in Nonlinear Analysis

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

Daciberg Lima Gonçalves, Dirceu Penteado, and João Peres Vieira

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Abstract

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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 33, Number 2 (2009), 293-305.

Dates
First available in Project Euclid: 27 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461785638

Mathematical Reviews number (MathSciNet)
MR2549619

Zentralblatt MATH identifier
1195.55003

Citation

Gonçalves, Daciberg Lima; Penteado, Dirceu; Vieira, João Peres. Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles. Topol. Methods Nonlinear Anal. 33 (2009), no. 2, 293--305. https://projecteuclid.org/euclid.tmna/1461785638


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