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On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces

  • Toshitake Kohno (a1)
Extract

The purpose of this paper is to establish the following isomorphism of Lie algebras.

Main Theorem. Let X be the complement of a hypersurface S in the complex projective space PN. Then the tower of nilpotent complex Lie algebras associated with the fundamental group π1(X, *) and the holonomy Lie algebra attached to S are isomorphic.

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References
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[Ko1] Kohno, T., Differential forms and the fundamental group of the complement of hypersurfaces, Proc. Pure Math. Amer. Math. Soc., 40 (1983), Part 1, 655662.
[Ko2] Kohno, T., Etude algébrique du groupe fondamental du complément d’une hypersurface et problèmes de K(π, 1) thèse de 3-ème cycle Université Paris VII, 1982.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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