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