Kyoto Journal of Mathematics

Partial holomorphic connections and extension of foliations

Isaia Nisoli

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Abstract

This paper stresses the strong link between the existence of partial holomorphic connections on the normal bundle of a foliation seen as a quotient of the ambient tangent bundle and the extendability of a foliation to an infinitesimal neighborhood of a submanifold. We find the obstructions to extendability, and thanks to the theory developed we obtain some new Khanedani–Lehmann–Suwa type index theorems.

Article information

Source
Kyoto J. Math., Volume 52, Number 3 (2012), 517-555.

Dates
First available in Project Euclid: 26 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1343309706

Digital Object Identifier
doi:10.1215/21562261-1625190

Mathematical Reviews number (MathSciNet)
MR2959947

Zentralblatt MATH identifier
1333.37066

Subjects
Primary: 37F75: Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]
Secondary: 32S65: Singularities of holomorphic vector fields and foliations 32A27: Local theory of residues [See also 32C30]

Citation

Nisoli, Isaia. Partial holomorphic connections and extension of foliations. Kyoto J. Math. 52 (2012), no. 3, 517--555. doi:10.1215/21562261-1625190. https://projecteuclid.org/euclid.kjm/1343309706


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