Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat connections and resonance varieties: from rank one to higher ranks   Given a finitely-generated group $\pi$ and a linear algebraic group $G$, the
representation variety Hom$(\pi,G)$ has a natural filtration by the
characteristic varieties associated to a rational representation of $G$. Its
algebraic counterpart, the space of $\mathfrak{g}$-valued flat connections on a
commutative, differential graded algebra $(A,d)$ admits a filtration by the
resonance varieties associated to a representation of $\mathfrak{g}$. We
establish here a number of results concerning the structure and qualitative
properties of these embedded resonance varieties, with particular attention to
the case when the rank 1 resonance variety decomposes as a finite union of
linear subspaces. The general theory is illustrated in detail in the case when
$\pi$ is either an Artin group, or the fundamental group of a smooth,
quasi-projective variety.

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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: cond-mat