Group theoretic perspective on Dehn fillings: Property P conjecture and beyond
Geometric Topology
2026-01-08 v1 Group Theory
Abstract
The Property P Conjecture, which was settled by Kronheimer and Mrowka, asserts that every --manifold obtained by non-trivial Dehn surgery on a non-trivial knot is never simply connected. We propose new perspectives in studying Dehn filling from group theoretic point of view, which stem from several variation of the Property P conjecture.
Cite
@article{arxiv.2601.03756,
title = {Group theoretic perspective on Dehn fillings: Property P conjecture and beyond},
author = {Tetsuya Ito and Kimihiko Motegi and Masakazu Teragaito},
journal= {arXiv preprint arXiv:2601.03756},
year = {2026}
}
Comments
22 pages, 3 figures, This paper is based on a lecture at MSJ-KMS Joint Meeting 2023. To appear in Springer Proc. Math. Stat., "Proceedings of the MSJ-KMS Joint Meeting 2023''. This paper is a companion to the paper: "Dehn filling and the knot group I: Realization property'' [Int. Math. Res. Not. IMRN, 2025, 1-31]