English

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.

Keywords

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