Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On infinitely generated homology of Torelli groups   Let $\mathcal{I}_g$ be the Torelli group of an oriented closed surface $S_g$
of genus $g$, that is, the kernel of the action of the mapping class group on
the first integral homology group of $S_g$. We prove that the $k$th integral
homology group of $\mathcal{I}_g$ contains a free abelian subgroup of infinite
rank, provided that $g\ge 3$ and $2g-3\le k\le 3g-6$. Earlier the same property
was known only for $k=3g-5$ (Bestvina, Bux, Margalit, 2007) and in the special
case $g=k=3$ (Johnson, Millson, 1992). We also show that the hyperelliptic
involution acts on the constructed infinite system of linearly independent
homology classes in $H_k(\mathcal{I}_g;\mathbb{Z})$ as multiplication by $-1$,
provided that $k+g$ is even, thus solving negatively a problem by Hain. For
$k=2g-3$, we show that the group $H_{2g-3}(\mathcal{I}_g;\mathbb{Z})$ contains
a free abelian subgroup of infinite rank generated by abelian cycles and we
construct explicitly an infinite system of abelian cycles generating such
subgroup. As a consequence of our results, we obtain that an Eilenberg-MacLane
CW-complex of type $K(\mathcal{I}_g,1)$ cannot have a finite $(2g-3)$-skeleton.
The proofs are based on the study of the Cartan-Leray spectral sequence for the
action of $\mathcal{I}_g$ on the complex of cycles constructed by Bestvina,
Bux, and Margalit.

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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con