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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The rational LS-category of $k$-trivial fibrations


Authors: Maxence Cuvilliez and Barry Jessup
Journal: Proc. Amer. Math. Soc. 131 (2003), 2223-2233
MSC (2000): Primary 53C29, 55M30, 55P62, 55R05
Published electronically: October 15, 2002
MathSciNet review: 1963771
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Abstract: We provide new upper and lower bounds for the rational LS-category of a rational fibration $\xi :F\to E \to K(\mathbf{Q},2n)$ of simply connected spaces that depend on a measure of the triviality of $\xi $ which is strictly finer than the vanishing of the higher holonomy actions. In particular, we prove that if $\xi $is $k$-trivial for some $k\ge 0$ and $H^{*}(F)$ enjoys Poincaré duality, then

\begin{displaymath}\operatorname{cat}_{0}E \ge \operatorname{cat}_{0}F +k.\end{displaymath}


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Additional Information

Maxence Cuvilliez
Affiliation: Centre de Recerca Matemàtica, Barcelona, Spain
Email: mcuvilli@crm.es

Barry Jessup
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Email: bjessup@uottawa.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06772-2
PII: S 0002-9939(02)06772-2
Keywords: Lusternik-Schnirelmann category, holonomy, minimal model
Received by editor(s): October 10, 2000
Received by editor(s) in revised form: February 21, 2002
Published electronically: October 15, 2002
Additional Notes: This research was partially supported by L’Université Catholique de Louvain-la-Neuve and by the National Science and Engineering Research Council of Canada. The second author thanks colleagues at UCL for their unstinting hospitality during a recent visit
Communicated by: Ralph Cohen
Article copyright: © Copyright 2002 American Mathematical Society