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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Morse theory on Kähler homogeneous spaces


Author: George D. Parker
Journal: Proc. Amer. Math. Soc. 34 (1972), 586-590
MSC: Primary 58E10; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9939-1972-0298705-1
MathSciNet review: 0298705
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Abstract: By exploiting the Kähler structure, we find a Morse function f on the homogeneous space $ \mathfrak{G}/C(\mathfrak{T}')$. The homology is readily computed and is seen to be contained in the diagram of $ \mathfrak{G}$. The Morse cells are shown to be complex analytic submanifolds and to coincide with those of a cell decomposition found by Borel in a different manner.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0298705-1
Keywords: Morse theory, Kähler manifold, homogeneous space, Killing field, Morse-Bott inequalities, infinitesimal diagram of $ \mathfrak{G}$, cell decomposition
Article copyright: © Copyright 1972 American Mathematical Society