Journal Article

Homotopy groups of complements and nonisolated singularities

Anatoly Libgober and Mihai Tibăr

in International Mathematics Research Notices

Volume 2002, issue 17, pages 871-888
Published in print January 2002 | ISSN: 1073-7928
Published online January 2002 | e-ISSN: 1687-0247 | DOI:
Homotopy groups of complements and nonisolated singularities

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We study the topology of the level sets f = t, where f = 0 has a nonisolated singularity, in two cases: f is a polynomial function on ℂn+1 with one atypical value, or f is a germ of a holomorphic function. In both cases we relate certain homology groups of the relevant level sets to the homotopy groups of complements of f = 0. As a consequence, we obtain the relationship between these homology groups and the data obtained from the “position of singularities” on a hyperplane section close to the hyperplane section passing through the singularity. We also obtain new vanishing results for the homotopy groups of the complements to affine hypersurfaces in ℂn+1, in terms of the behavior at infinity.

Journal Article.  0 words. 

Subjects: Mathematics

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