Noncritical holomorphic functions on Stein manifolds

@article{Forstneri2002NoncriticalHF,
  title={Noncritical holomorphic functions on Stein manifolds},
  author={Franc Forstneri{\vc}},
  journal={Acta Mathematica},
  year={2002},
  volume={191},
  pages={143-189}
}
We prove that every Stein manifold X of dimension n admits [(n+1)/2] holomorphic functions with pointwise independent differentials, and this number is maximal for every n. In particular, X admits a holomorphic function without critical points; this extends a result of Gunning and Narasimhan from 1967 who constructed such functions on open Riemann surfaces. Furthermore, every surjective complex vector bundle map from the tangent bundle TX onto the trivial bundle of rank q < n=dim X is homotopic… CONTINUE READING

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