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The sectional category of spherical fibrations

Author: Don Stanley
Journal: Proc. Amer. Math. Soc. 128 (2000), 3137-3143
MSC (1991): Primary 55R25, 55P62; Secondary 55M30
Published electronically: April 28, 2000
MathSciNet review: 1691006
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We give homological conditions which determine sectional category, secat, for rational spherical fibrations. In the odd dimensional case the secat is the least power of the Euler class which is trivial. In the even dimensional case secat is one when a certain homology class in twice the dimension of the sphere is $-1$ times a square. Otherwise secat is two. We apply our results to construct a fibration $p$ such that $\mathrm{secat}(p)=2$ and genus $(p)=\infty$. We also observe that secat, unlike cat, can decrease in a field extension of $\mathbb{Q} $.

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Additional Information

Don Stanley
Affiliation: II Mathematisches Institut, Freie Univerität Berlin, Arnimallee 3, D-14195 Berlin, Germany
Address at time of publication: Max-Plank-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany

Keywords: Sectional category, spherical fibrations, rational homotopy theory, Lusternik-Schnirelmann category
Received by editor(s): December 10, 1998
Published electronically: April 28, 2000
Additional Notes: This work was supported by DFG grant Sche 328/2-1
Dedicated: This paper is dedicated to my son Russell
Communicated by: Ralph L. Cohen
Article copyright: © Copyright 2000 American Mathematical Society

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