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Some examples of minimally degenerate Morse functions

Published online by Cambridge University Press:  20 January 2009

Frances Kirwan
Frances Kirwan
Affiliation:
Mathematical Institute, St Giles, Oxford
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Let X be a compact Riemannian manifold. If f:X→ℝ is a nondegenerate Morse function in the sense of Bott [2] then one has Morse inequalities which can be expressed in the form

where Pt(X) is the Poincaré polynomial Σtidim Hi(X;ℚ of X ann {Cβ|β ∈B} are the connected components of the set of critical points for f For any polynomial Q(t)∈ℤ[t] we write Q(t)≧0 if all the coefficients of Q are nonnegative.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 2 , June 1987 , pp. 289 - 293
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

1.Atiyah, M. F., Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1–15.CrossRefGoogle Scholar
2.Bott, R., Nondegenerate critical manifolds, Ann. of Math. 60 (1954), 248–261.CrossRefGoogle Scholar
3.Kirwan, F. C., Cohomology of quotients in algebraic and symplectic geometry (Mathematical Notes 31, Princeton, 1985).Google Scholar