Evaluation subgroups of homogeneous spaces of compact Lie groups (Q2873009)
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scientific article; zbMATH DE number 6247115
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Evaluation subgroups of homogeneous spaces of compact Lie groups |
scientific article; zbMATH DE number 6247115 |
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17 January 2014
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evaluation subgroup
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symmetric spaces
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stable homotopy groups
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0.8990042
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0.89661914
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0.89655167
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0.8957382
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0.89218867
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Evaluation subgroups of homogeneous spaces of compact Lie groups (English)
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Two famous papers of \textit{D. H. Gottlieb} [Am. J. Math. 87, 840--856 (1965; Zbl 0148.17106)] and [ibid. 91, 729--756 (1969; Zbl 0185.27102)] initiated the study of evaluation subgroups of homotopy groups. These subgroups, now called Gottlieb groups, have not been easy to calculate.NEWLINENEWLINEThe purpose of this paper is to estimate and calculate the Gottlieb groups of homogeneous spaces, particularly the irreducible symmetric spaces, and specifically the eight classical types classified by E. Cartan. The method uses the result of \textit{J. Siegel} [Pac. J. Math. 31, 209--214 (1969; Zbl 0183.51701)]. That paper estimates, from below, the Gottlieb group of a symmetric group in terms of the image, on homotopy groups, of the projection of the homotopy group of the Lie group to the homogeneous space. In some cases, the estimate is exact, while in other cases, the Gottlieb group may still be determined with other information.
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