Integrable Gradient Flows and Morse Theory

Details Integrable Gradient Flows and Morse Theory Integrable Gradient Flows and Morse Theory

1995-06-09

arxiv.org/abs/dg-ga/9506004v2

Mathematics

Differential Geometry

20 pages, La-TeX, revised 26 Sept 95: some mistakes corrected, examples and references added

Scientific paper

Examples of Morse functions with integrable gradient flows on some classical Riemannian manifolds are considered. In particular, we show that a generic height function on the symmetric embeddings of classical Lie groups and certain symmetric spaces is a perfect Morse function, i.e. has as many critical points as the homology requires, and the corresponding gradient flow can be described explicitly. This gives an explicit cell decomposition and geometric realization of the homology for such a manifold. As another application of the integrable Morse functions we give an elementary proof of Vassiljev's theorem on the flag join of Grassmannians.

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