Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operads, deformation theory and F-manifolds   It is shown that every algebra over the chain operad of the little disks
operad gives naturally rise to a Hertling-Manin's F-manifold, that is a smooth
manifold equipped with an integrable graded commutative associative product on
the tangent sheaf. In particular, moduli spaces of extended deformations of
complex/symplectic structures are shown to have a canonical structure of
F-manifold. With the help of the $G_\infty$-operad a strong homotopy version of
the notion of F-manifold is constructed. Among natural examples of
$F_\infty$-manifolds one finds formal manifolds associated with the Hochschild
cohomology of an associative algebra and with the singular cohomology of an
arbitrary compact topological space.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph