Group theoretic perspective on Dehn fillings: Property P conjecture and beyond

Tetsuya Ito; Kimihiko Motegi; Masakazu Teragaito

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arXiv · 2601.03756

Group theoretic perspective on Dehn fillings: Property P conjecture and beyond

Tetsuya Ito·Kimihiko Motegi·Masakazu Teragaito

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Abstract

The Property P Conjecture, which was settled by Kronheimer and Mrowka, asserts that every $3$--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.

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Tetsuya Ito, Kimihiko Motegi, Masakazu Teragaito. 2026-01-07. Group theoretic perspective on Dehn fillings: Property P conjecture and beyond. https://arxiv.org/abs/2601.03756

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