Quickly unknotting topological spheres
نویسندگان
چکیده
منابع مشابه
Unknotting 3-spheres in Six Dimensions
Haefliger [2] has shown that a differentiable embedding of the 3-sphere S3 in euclidean 6-dimensions El can be differentiably knotted. On the other hand any piecewise linear embedding of Sn in Ek is combinatorially unknotted if k^n + 3 (see [5; 6; 7]). The case S3 in E6 appears to be the first occasion on which the differentiable and combinatorial theories of isotopy differ. Therefore it seemed...
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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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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 us observe that ∅ is ∅-valued and ∅ is onto. Next we state three propositions: (1) For every function f and for every set Y holds dom(Y f) = f−1(Y ). (2) For every function f and for all sets Y1, Y2 such that Y2 ⊆ Y1 holds (Y1 f)(Y2) = f(Y2). (3) Let S, T be topological structures and f be a function from S into T . If f is homeomorphism, then f−1 is homeomorphism. Let S, T be topological s...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0507349-0