Partial holomorphic connections and extension of foliations

Details Partial holomorphic connections and extension of foliations Partial holomorphic connections and extension of foliations

2010-10-17

arxiv.org/abs/1010.3450v2

Mathematics

Complex Variables

Scientific paper

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.

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