Estimating the rational LS-category of elliptic spaces

Ghorbal, Sonia; Jessup, Barry

doi:10.1090/S0002-9939-00-05739-7

Estimating the rational LS-category of elliptic spaces
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by Sonia Ghorbal and Barry Jessup PDF

Proc. Amer. Math. Soc. 129 (2001), 1833-1842 Request permission

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, \[ \operatorname {cat}_{0} S \ge \dim L_{S}^{\mathrm {ev}} +\operatorname {dim} ZL_{S}^{\mathrm {odd}},\] 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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