Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbits of curves under the Johnson kernel   This paper has two main goals. First, we give a complete, explicit, and
computable solution to the problem of when two simple closed curves on a
surface are equivalent under the Johnson kernel. Second, we show that the
Johnson filtration and the Johnson homomorphism can be defined intrinsically on
subsurfaces and prove that both are functorial under inclusions of subsurfaces.
The key point is that the latter reduces the former to a finite computation,
which can be carried out by hand. In particular this solves the conjugacy
problem in the Johnson kernel for separating twists. Using a theorem of Putman,
we compute the first Betti number of the Torelli group of a subsurface.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph