The rational LS-category of $k$-trivial fibrations
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- by Maxence Cuvilliez and Barry Jessup PDF
- Proc. Amer. Math. Soc. 131 (2003), 2223-2233 Request permission
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{equation*}\operatorname {cat}_{0}E \ge \operatorname {cat}_{0}F +k.\end{equation*}References
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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
- MR Author ID: 265531
- Email: bjessup@uottawa.ca
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2223-2233
- MSC (2000): Primary 53C29, 55M30, 55P62, 55R05
- DOI: https://doi.org/10.1090/S0002-9939-02-06772-2
- MathSciNet review: 1963771