This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
@article{bwmeta1.element.bwnjournal-article-bcpv45i1p25bwm,
author = {Bryden, J. and Zvengrowski, P.},
title = {The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {25-39},
zbl = {0939.57018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p25bwm}
}
Bryden, J.; Zvengrowski, P. The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category. Banach Center Publications, Tome 43 (1998) pp. 25-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p25bwm/
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