Morse theory on Kähler homogeneous spaces

Parker, George D.

doi:10.1090/S0002-9939-1972-0298705-1

Morse theory on Kähler homogeneous spaces
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Proc. Amer. Math. Soc. 34 (1972), 586-590 Request permission

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.

References

Armand Borel, Kählerian coset spaces of semisimple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1147–1151. MR 77878, DOI 10.1073/pnas.40.12.1147
A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458–538. MR 102800, DOI 10.2307/2372795
Raoul Bott, An application of the Morse theory to the topology of Lie-groups, Bull. Soc. Math. France 84 (1956), 251–281. MR 87035, DOI 10.24033/bsmf.1472
Raoul Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248–261. MR 64399, DOI 10.2307/1969631
Theodore Frankel, Fixed points and torsion on Kähler manifolds, Ann. of Math. (2) 70 (1959), 1–8. MR 131883, DOI 10.2307/1969889
Alfred Frölicher, Zur Differentialgeometrie der komplexen Strukturen, Math. Ann. 129 (1955), 50–95 (German). MR 68282, DOI 10.1007/BF01362360
Harish-Chandra, On a lemma of F. Bruhat, J. Math. Pures Appl. (9) 35 (1956), 203–210. MR 79728