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

 

Estimating the rational LS-category of elliptic spaces


Authors: Sonia Ghorbal and Barry Jessup
Journal: Proc. Amer. Math. Soc. 129 (2001), 1833-1842
MSC (2000): Primary 55P62
Published electronically: October 31, 2000
MathSciNet review: 1814117
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Abstract: An elliptic space is one whose rational homotopy and rational cohomology are both finite dimensional. We prove, for Toomer's invariant, two improvements of the estimate of the Mapping theorem relying on data from the homotopy Lie algebra of the space. In particular, we show that if $S$ is elliptic,


\begin{displaymath}\text{\rm cat}_{0} S \ge \dim L_{S}^{\text{\rm ev}} +\operatorname{dim} ZL_{S}^{\text{odd}},\end{displaymath}

where $L_{S}$ is the rational homotopy Lie algebra of $S$ and $ZL_{S}$ its centre.

Several interesting examples are presented to illustrate our results.


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Additional Information

Sonia Ghorbal
Affiliation: Institut Préparatoire aux Études d’ingénieurs de Sousse, Tunisie
Email: Sonia.Ghorbal@ipeiss.rnu.tn

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/S0002-9939-00-05739-7
PII: S 0002-9939(00)05739-7
Keywords: Elliptic spaces, minimal models, rational category
Received by editor(s): September 15, 1999
Published electronically: October 31, 2000
Additional Notes: This research was partially supported by a UCL postdoctoral grant, the University of Ottawa and the National Science and Engineering Research Council of Canada.
The second author also acknowledges the support of the National Science and Engineering Research Council of Canada.
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society