Twisted Picard-Lefschetz formulas

DOI10.1007/BF01077718zbMath0665.32011OpenAlexW1966426756MaRDI QIDQ1115995

Alexander Givental

Publication date: 1988

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01077718

zbMATH Keywords

cohomology groupstwisted cohomologymonodromyfundamental groupvanishing cyclesisolated hypersurface singularitiesversal deformationPicard-Lefschetz theory

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Deformations of complex singularities; vanishing cycles (32S30) Complex singularities (32Sxx)

Related Items

Picard–Lefschetz theory and dilating ℂ*-actions, Fundamental group of discriminant complements of Brieskorn-Pham polynomials, Picard-Lefschetz theory for the universal coverings of complements to affine hypersurfaces, Integrable hierarchies and the mirror model of local \({\mathbb {CP}}^{1}\), Symplectic cohomology and \(q\)-intersection numbers, Vanishing cycles and Cartan eigenvectors, 4-dimensional Frobenius manifolds and Painlevé VI, Discriminant complements and kernels of monodromy representations, Elliptic root system and elliptic Artin group., Distinguished Bases and Monodromy of Complex Hypersurface Singularities

Cites Work

• Semicontinuity of the singularity spectrum
• Discrete groups of reflections in the complex ball
• Normal forms of the degrees of a volume form
• Monodromy representations of braid groups and Yang-Baxter equations
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• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
• Cross ratio of a nondegenerate quadruple of subspaces
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