Abstract
Abstract
The Torelli group of a closed oriented surface
of genus
is the subgroup
of the mapping class group
consisting of all mapping classes that act trivially on the homology of
. One of the most intriguing open problems concerning Torelli groups is the question of whether the group
is finitely presented. A possible approach to this problem relies on the study of the second homology group of
using the spectral sequence
for the action of
on the complex of cycles. In this paper we obtain evidence for the conjecture that
is not finitely generated and hence
is not finitely presented. Namely, we prove that the term
of the spectral sequence is not finitely generated, that is, the group
remains infinitely generated after taking quotients by the images of the differentials
and
. Proving that it remains infinitely generated after taking the quotient by the image of
would complete the proof that
is not finitely presented.
Funder
Russian Science Foundation
Cited by
1 articles.
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