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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-1,
author = {D. L. Gon\c calves and D. Penteado and J. P. Vieira},
title = {Fixed points on torus fiber bundles over the circle},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {1-38},
zbl = {1060.55001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-1}
}
D. L. Gonçalves; D. Penteado; J. P. Vieira. Fixed points on torus fiber bundles over the circle. Fundamenta Mathematicae, Tome 184 (2004) pp. 1-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-1-1/