Geodesic
Fixed points on Klein bottle fiber bundles over the circle
D. L. Gonçalves 1   ; D. Penteado 2   ; J. P. Vieira 3
1 Departamento de Matemática IME – USP Caixa Postal 66.281 CEP 05314-970, São Paulo, SP, 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, São Paulo State University – UNESP Caixa Postal 178 Rio Claro 13500-230, Brazil
Fundamenta Mathematicae, Tome 203 (2009) no. 3, pp. 263-292 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 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.
DOI : 10.4064/fm203-3-3
Keywords: main purpose work study fixed points fiber preserving maps circle spaces which fiber bundles fiber klein bottle classify maps which deformed fiberwise fixed point map similar problem torus fiber bundles has solved recently

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

1 Departamento de Matemática IME – USP Caixa Postal 66.281 CEP 05314-970, São Paulo, SP, 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, São Paulo State University – UNESP Caixa Postal 178 Rio Claro 13500-230, Brazil 
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     title = {Fixed points on {Klein} bottle fiber bundles over the circle},
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D. L. Gonçalves; D. Penteado; J. P. Vieira. Fixed points on Klein bottle fiber bundles over the circle. Fundamenta Mathematicae, Tome 203 (2009) no. 3, pp. 263-292. doi: 10.4064/fm203-3-3

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