Knots with unknotting number 1 and essential Conway spheres
نویسندگان
چکیده
منابع مشابه
Knots with Unknotting Number 1 and Essential Conway Spheres
For a knot K in S, let T(K) be the characteristic toric sub-orbifold of the orbifold (S, K) as defined by Bonahon-Siebenmann. If K has unknotting number one, we show that an unknotting arc for K can always be found which is disjoint from T(K), unless either K is an EM-knot (of Eudave-Muñoz) or (S,K) contains an EM-tangle after cutting along T(K). As a consequence, we describe exactly which larg...
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We use Heegaard Floer homology to give obstructions to unknotting a knot with a single crossing change. These restrictions are particularly useful in the case where the knot in question is alternating. As an example, we use them to classify all knots with crossing number less than or equal to nine and unknotting number equal to one. We also classify alternating knots with ten crossings and unkn...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2006
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2006.6.2051