Fixed points on Klein bottle fiber bundles over the circle

Tom 203 / 2009

D. L. Gonçalves, D. Penteado, J. P. Vieira Fundamenta Mathematicae 203 (2009), 263-292 MSC: Primary 55M20; Secondary 55R10, 55S35. DOI: 10.4064/fm203-3-3

Streszczenie

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle $S^1$ for spaces which are fiber bundles over $S^1$ and the fiber is the Klein bottle $K$. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over $S^{1}$ has been solved recently.

Autorzy

  • D. L. GonçalvesDepartamento de Matemática
    IME – USP
    Caixa Postal 66.281
    CEP 05314-970, São Paulo, SP, Brazil
    e-mail
  • D. PenteadoDepartamento de Matemática
    Universidade Federal de São Carlos
    Rodovia Washington Luiz, Km 235
    São Carlos 13565-905, Brazil
    e-mail
  • J. P. VieiraDepartamento de Matemática
    I.G.C.E, São Paulo State University – UNESP
    Caixa Postal 178
    Rio Claro 13500-230, Brazil
    e-mail

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