Gauss–Manin connections for boundary singularities and isochore deformations

• Autorzy: Kourliouros K.
• Języki publikacji: EN

Abstrakty

EN

We study here the relative cohomology and the Gauss–Manin connections associated to an isolated singularity of a function on a manifold with boundary, i.e. with a fixed hyperplane section. We prove several relative analogs of classical theorems obtained mainly by E. Brieskorn and B. Malgrange, concerning the properties of the Gauss–Manin connection as well as its relations with the Picard–Lefschetz monodromy and the asymptotics of integrals of holomorphic forms along the vanishing cycles. Finally, we give an application in isochore deformation theory, i.e. the deformation theory of boundary singularities with respect to a volume form. In particular, we prove the relative analog of J. Vey’s isochore Morse lemma, J.-P. Françoise’s generalisation on the local normal forms of volume forms with respect to the boundary singularity-preserving diffeomorphisms, as well as M. D. Garay’s theorem on the isochore version of Mather’s versal unfolding theorem.

Słowa kluczowe

EN

boundary singularities; Gauss-Manin connections; relative de Rham cohomology; volume forms; isochore geometry; normal forms

PL

punkty osobliwe izolowane; koneksje Gaussa-Manina; analiza zespolona

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 2
• Strony: 250--288
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Kourliouros K.

• Imperial College London, United Kingdom

Bibliografia

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