Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separating twists and the Magnus representation of the Torelli group   The Magnus representation of the Torelli subgroup of the mapping class group
of a surface is a homomorphism r: I_{g,1} -> GL_{2g}(Z[H]). Here H is the first
homology group of the surface. This representation is not faithful; in
particular, Suzuki previously described precisely when the commutator of two
Dehn twists about separating curves is in the kernel of r. Using the trace of
the Magnus representation, we apply a new method of showing that two
endomorphisms generate a free group to prove that the images of two positive
separating multitwists under the Magnus representation either commute or
generate a free group, and we characterize when each case occurs.

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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg