Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: (T)-structures over 2-dimensional F-manifolds: formal classification   A $(TE)$-structure $\nabla$ over a complex manifold $M$ is a meromorphic
connection defined on a holomorphic vector bundle over $\mathbb{C}\times M$,
with poles of Poincar\'e rank one along $\{ 0 \} \times M.$ Under a mild
additional condition (the so called unfolding condition), $\nabla$ induces a
multiplication on $TM$ and a vector field on $M$ (the Euler field), which make
$M$ into an $F$-manifold with Euler field. By taking the pull-backs of $\nabla$
under the inclusions $\{ z\} \times M \rightarrow \mathbb{C}\times M$ we obtain
a family of flat connections on vector bundles over $M$, parameterized by $z\in
\mathbb{C}^{*}$. The properties of such a family of connections give rise to
the notion of $(T)$-structure. Therefore, any $(TE)$-structure underlies a
$(T)$-structure but the converse is not true. The unfolding condition can be
defined also for $(T)$-structures. A $(T)$-structure with the unfolding
condition induces on its parameter space the structure of an $F$-manifold
(without Euler field). After a brief review on the theory of $(T)$ and
$(TE)$-structures, we determine normal forms for the equivalence classes, under
formal isomorphisms, of $(T)$-structures which induce a given irreducible germ
of $2$-dimensional $F$-manifolds.

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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas