Group Theoretic Perspective on Dehn Fillings: Property P Conjecture and Beyond
摘要
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.