Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The basic $dd^{\mathcal{J}}$-lemma   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.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol