Fixed points on torus fiber bundles over the circle
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Polish Acad Sciences Inst Mathematics
Institute of Mathematics, Polish Academy of Sciences
Institute of Mathematics, Polish Academy of Sciences
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The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.
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Fundamenta Mathematicae. Warsaw: Polish Acad Sciences Inst Mathematics, v. 183, n. 1, p. 1-38, 2004.
