Finiteness properties of the Torelli group of surfaces with 2 boundary components

Charalampos Stylianakis

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arXiv · 2601.05834

Finiteness properties of the Torelli group of surfaces with 2 boundary components

Charalampos Stylianakis

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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 kernel is finitely generated if the genus of the surface is at least 5 and has 2 boundary components.

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Charalampos Stylianakis. 2026-01-09. Finiteness properties of the Torelli group of surfaces with 2 boundary components. https://arxiv.org/abs/2601.05834

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