منابع مشابه
Exceptional Surgery on Knots
Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a nonboundary-parallel, incompressible torus and is not a generalized 1-iterated torus knot complement, t...
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We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.
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There is no known algorithm for determining whether a knot has unknotting number one, practical or otherwise. Indeed, there are many explicit knots (11328 for example) that are conjectured to have unknotting number two, but for which no proof of this fact is currently available. For many years, the knot 810 was in this class, but a celebrated application of Heegaard Floer homology by Ozsváth an...
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Let Y be a closed oriented three-manifold and K be a framed knot in Y . For a rational number r , let Yr(K) be the resulting manifold obtained by Dehn surgery along K with slope r with respect to the given framing. For a knot K in S3 , we will always use the Seifert framing. Two surgeries along K with distinct slopes r and s are called cosmetic if Yr(K) and Ys(K) are homeomorphic. The two surge...
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We classify all knot diagrams of genus two and three, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3and 4-move conjectures, and the calculation of the maximal hyperbolic volume for weak genus two knots. We also study the values of the link polynomial...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0438322-8