Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characteristic forms for holomorphic families of local systems   Let $f:\mathcal{X}\to S$ be a proper holomorphic submersion of complex
manifolds and $G$ a complex reductive linear algebraic group with Lie algebra
$\mathfrak{g}$. Assume also given a holomorphic principal $G$-bundle
$\mathcal{P}$ over $\mathcal{X}$ which is endowed with a holomorphic connection
$\nabla$ relative to $f$ that is flat (this to be thought of as a holomorphic
family of compact complex manifolds endowed with a holomorphic principal
$G$-bundle with flat connection). We show that a refinement of the Chern-Weil
homomorphism yields a graded algebra homomorphism
$\mathbb{C}[\mathfrak{g}]^G\to \bigoplus_{n\ge 0}
H^0(S,\,\Omega^n_{S,cl}\otimes R^nf_*\mathbb{C})$, where $\Omega^n_{S,cl}$
stands for the sheaf of closed holomorphic $n$-forms on $S$. If the fibers of
$f$ are compact Riemann surfaces and we take as our invariant the Killing form,
then we recover Goldman's closed holomorphic $2$-form on the base $S$.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys