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arXiv · 1609.04539

The basic $dd^{\mathcal{J}}$-lemma

Pawel Razny
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Abstract

The purpose of this short paper is to further develop the theory of transverse generalized complex structures. We focus on proving some equivalent conditions to the basic $dd^{\mathcal{J}}$ -lemma. We justify our approach by describing the transverse symplectic structure in this language and relating the basic $dd^{\mathcal{J}}$-lemma to the surjectivity of the Lefschetz map. We also present a non-trivial example of a foliation endowed with a transverse generalized complex structure. Transverse generalized complex structures do not rely heavily on the existence of a bundle-like metric, which makes them a convienient tool to study some non-Riemmanian foliations.

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Pawel Razny. 2016-09-15. The basic $dd^{\mathcal{J}}$-lemma. https://arxiv.org/abs/1609.04539

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