Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double Johnson filtrations for mapping class groups   We first develop a general theory of Johnson filtrations and Johnson
homomorphisms for a group $G$ acting on another group $K$ equipped with a
filtration indexed by a "good" ordered commutative monoid. Then, specializing
it to the case where the monoid is the additive monoid $\mathbb{N}^2$ of pairs
on nonnegative integers, we obtain a theory of double Johnson filtrations and
homomorphisms. We apply this theory to the mapping class group $\mathcal{M}$ of
a surface $\Sigma_{g,1}$ with one boundary component, equipped with the normal
subgroups $\bar{X}$, $\bar{Y}$ of $\pi_1(\Sigma_{g,1})$ associated to a
standard Heegaard splitting of the $3$-sphere. We also consider the case where
the group $G$ is the automorphism group of a free group.

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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio