Abstract
A partial generalization of Sophus Lie’s triangular form for solvable Lie algebras is presented. As application one is led to an iterated fibration for arbitrary homogeneous spaces. In the case of compact homogeneous spaces, one concludes easily that the Euler number is ≥0.
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References
C. Chevalley (1941) ArticleTitleOn the topological structure of solvable groups Ann. of Math. 42 668–675
C. Chevalley (1951) Theorie des groupes de Lie 2 Hermann Paris 2
S. Helgason (1962) Differential Geometry and Symmetric Spaces Academic Press New York
H. Hopf (1926) ArticleTitleVektorfelder in n-dimensionalen Mannigfaltigkeiten Math. Annal. 96 225–250 Occurrence Handle10.1007/BF01209164
Hopf, H. and Samelson, H.: Ein Satz über die Werkungraüme geschbossener Liesche Gruppen, Comment Math. Helv. 13 (1940-41), 240–251.
Hirsch, M. W. and Robbin, J.: Private Communication.
D. Montgomery (1950) ArticleTitleSimply connected homogeneous spaces Proc. Amer. Math. Soc. 1 467–469
Mostow, G. D.: Extensibility of local Lie groups of transformations and groups on surfaces, Ann. of Math. 52 (1950).
G. D. Mostow (1954) ArticleTitleFactor spaces of solvable groups Ann. of Math. 60 1–27
G. D. Mostow (1956) ArticleTitleFully reducible subgroups of algebraic groups Amer. J. Math. 78 200–221
G. D. Mostow (1962) ArticleTitleCovariant fiberings of Klein spaces II Amer. J. Math 84 466–474
Serre, J. P.: Homologie singulière des espaces fibrés, Ann. of Math. (2), 54, 425–505.
A. Weil (1935) ArticleTitleDémonstration topologique d’un théorème fondamental de Cartan Collected Papers Acad. Sci. Paris 200 518–520
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Mostow, G.D. A Structure Theorem for Homogeneous Spaces. Geom Dedicata 114, 87–102 (2005). https://doi.org/10.1007/s10711-004-1675-9
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DOI: https://doi.org/10.1007/s10711-004-1675-9