Fixed points on torus fiber bundles over the circle

D. L. Gonçalves, D. Penteado, and J. P. Vieira. "Fixed points on torus fiber bundles over the circle." Fundamenta Mathematicae 183.1 (2004): 1-38. <http://eudml.org/doc/283354>.

@article{D2004,
abstract = {The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fibrations over S¹ 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 S¹ to a fixed point free map. For the case where the fiber is a torus, we classify all maps over S¹ which can be deformed fiberwise to a fixed point free map.},
author = {D. L. Gonçalves, D. Penteado, J. P. Vieira},
journal = {Fundamenta Mathematicae},
keywords = {fixed point; fiber bundle; fiberwise homotopy; abelianized obstruction},
language = {eng},
number = {1},
pages = {1-38},
title = {Fixed points on torus fiber bundles over the circle},
url = {http://eudml.org/doc/283354},
volume = {183},
year = {2004},
}

TY - JOUR
AU - D. L. Gonçalves
AU - D. Penteado
AU - J. P. Vieira
TI - Fixed points on torus fiber bundles over the circle
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 1
SP - 1
EP - 38
AB - The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fibrations over S¹ 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 S¹ to a fixed point free map. For the case where the fiber is a torus, we classify all maps over S¹ which can be deformed fiberwise to a fixed point free map.
LA - eng
KW - fixed point; fiber bundle; fiberwise homotopy; abelianized obstruction
UR - http://eudml.org/doc/283354
ER -