Finiteness properties of the Torelli group of surfaces with 2 boundary components
Geometric Topology
2026-01-12 v1 Group Theory
Abstract
In this paper we prove that the Torelli group of a surface of genus at least 3 with 2 boundary components is finitely generated. As a consequence, we answer Putman's question on the finite generation of the stabilizer subgroup of the Torelli group of a non separating simple closed curve. Furthermore, we prove that the Johnson's kernel is finitely generated if the genus of the surface is at least 5.
Cite
@article{arxiv.2601.05834,
title = {Finiteness properties of the Torelli group of surfaces with 2 boundary components},
author = {Charalampos Stylianakis},
journal= {arXiv preprint arXiv:2601.05834},
year = {2026}
}
Comments
22 pages, 8 Figures