Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cobordism group of homology cylinders   Garoufalidis and Levine introduced the homology cobordism group of homology
cylinders over a surface. This group can be regarded as a generalization of the
mapping class group. Using torsion invariants, we show that the abelianization
of this group is infinitely generated provided that the first Betti number of
the surface is positive. In particular, this shows that the group is not
perfect. This answers questions of Garoufalidis-Levine and Goda-Sakasai.
Furthermore we show that the abelianization of the group has infinite rank for
the case that the surface has more than one boundary component. These results
hold for the homology cylinder analogue of the Torelli group as well.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci