Fixed points on torus fiber bundles over the circle

Volume 183 / 2004

D. L. Gonçalves, D. Penteado, J. P. Vieira Fundamenta Mathematicae 183 (2004), 1-38 MSC: Primary 55M20; Secondary 55R10. DOI: 10.4064/fm183-1-1


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.


  • D. L. GonçalvesDepartamento de Matemática
    Caixa Postal 66.281
    São Paulo 05311-970, Brazil
  • D. PenteadoDepartamento de Matemática
    Universidade Federal de São Carlos
    Rodovia Washington Luiz, Km 235
    São Carlos 13565-905, Brazil
  • J. P. VieiraDepartamento de Matemática
    Caixa Postal 178
    Rio Claro 13500-230, Brazil

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