Geodesic
Fixed points on torus fiber bundles over the circle
D. L. Gonçalves1 ; D. Penteado2 ; J. P. Vieira3
1 Departamento de Matemática IME–USP Caixa Postal 66.281 São Paulo 05311-970, Brazil
2 Departamento de Matemática Universidade Federal de São Carlos Rodovia Washington Luiz, Km 235 São Carlos 13565-905, Brazil
3 Departamento de Matemática I.G.C.E–UNESP Caixa Postal 178 Rio Claro 13500-230, Brazil
Fundamenta Mathematicae, Tome 183 (2004) no. 1, pp. 1-38 Cet article a éte moissonné depuis la source 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 are 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.
DOI : 10.4064/fm183-1-1
Keywords: main purpose work study fixed points fiber preserving maps circle spaces which fibrations fiber torus nbsp where fiber surface nonpositive euler characteristic establish general algebraic conditions terms fundamental group induced homomorphism existence deformation map fixed point map where fiber torus classify maps which deformed fiberwise fixed point map

D. L. Gonçalves 1 ; D. Penteado 2 ; J. P. Vieira 3

1 Departamento de Matemática IME–USP Caixa Postal 66.281 São Paulo 05311-970, Brazil
2 Departamento de Matemática Universidade Federal de São Carlos Rodovia Washington Luiz, Km 235 São Carlos 13565-905, Brazil
3 Departamento de Matemática I.G.C.E–UNESP Caixa Postal 178 Rio Claro 13500-230, Brazil 
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D. L. Gonçalves; D. Penteado; J. P. Vieira. Fixed points on torus fiber bundles over the circle. Fundamenta Mathematicae, Tome 183 (2004) no. 1, pp. 1-38. doi: 10.4064/fm183-1-1

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