Reducing Dehn filling and toroidal Dehn filling
نویسنده
چکیده
It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is shown to hold for genus 1 knots in the 3-sphere. ~e~~~~: Dehn filling; Reducible slope; Essential torus slope; Cabling conjecture AMS classijicatian: 57M25; 57R65
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