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, cat(o)S greater than or equal to dim L-S(ev) + dim ZL(S)(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. [References: 19]
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机译：椭圆空间是有理同伦和有理同调都是有限维的空间。对于Toomer的不变量，我们证明了Maping定理的估计有两个改进，它依赖于来自空间同伦李代数的数据。特别地，我们表明如果S是椭圆形，则cat（o）S大于或等于dim LS（ev）+ dim ZL（S）（odd），其中LS是S和ZL（S）的有理同伦李代数）其中心。提出了几个有趣的例子来说明我们的结果。 [参考：19]
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