The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fiber bundles over S¹ 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 S¹ has been solved recently.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-3-3,
author = {D. L. Gon\c calves and D. Penteado and J. P. Vieira},
title = {Fixed points on Klein bottle fiber bundles over the circle},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {263-292},
zbl = {1167.55001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-3-3}
}
D. L. Gonçalves; D. Penteado; J. P. Vieira. Fixed points on Klein bottle fiber bundles over the circle. Fundamenta Mathematicae, Tome 205 (2009) pp. 263-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-3-3/