Holomorphic Morse Inequalities

@inproceedings{DEMAILLY1991HolomorphicMI,
  title={Holomorphic Morse Inequalities},
  author={Jean-Pierre DEMAILLY},
  year={1991}
}
  • Jean-Pierre DEMAILLY
  • Published 1991
Let M be a compact C manifold, dimR M = m, and h a Morse function, i.e. a function such that all critical points are non degenerate. The standard Morse inequalities relate the Betti numbers bq = dimH q DR(M,R) and the numbers sq = # critical points of index q , where the index of a critical point is the number of negative eigenvalues of the Hessian form (∂h/∂xi∂xj). Specifically, the following “strong Morse inequalities” hold : 
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