Gauss-Manin Connections for Boundary Singularities and Isochore Deformations

Abstract: 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. Fran~oise'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 versa! unfolding theorem.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Gauss-Manin Connections for Boundary Singularities and Isochore Deformations ; volume:48 ; number:2 ; year:2015 ; pages:250-288 ; extent:39 ; Demonstratio mathematica ; 48, Heft 2 (2015), 250-288 (gesamt 39)

Contributors, Places and Time

• Creator: Kourliouros, Konstantinos

Further information

• DOI: 10.1515/dema-2015-0020
• URN: urn:nbn:de:101:1-2411181442283.534776385427
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:31 AM CEST