منابع مشابه
Twisting Spun Knots
1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show that Mazur's example is in fact a true 4-sphere after all. This raises the odds in favour of the 4-dimensional Poincaré Conjecture. The proof involves a smooth knot of S2 in S4 with unusual properties.
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Surveying the results of three recent papers and some currently ongoing research, we show how a generalization of Brylawski’s tensor product formula to colored graphs may be used to compute the Jones polynomial of some fairly complicated knots and, in the future, even virtual knots. Résumé. En faisant une revue de trois articles récents et de la recherche en cours, nous montrons comment une gén...
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One of the most basic questions in knot theory remains unresolved: is crossing number additive under connected sum? In other words, does the equality c(K1♯K2) = c(K1) + c(K2) always hold, where c(K) denotes the crossing number of a knot K and K1♯K2 is the connected sum of two (oriented) knots K1 and K2? The inequality c(K1♯K2) ≤ c(K1) + c(K2) is trivial, but very little more is known in general...
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We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in [15] naturally admits an integer graded lifting, and it formulates a filtration and induced spectral sequence. Such a spectral sequence converges to the symplectic homology of knots in [15]. We show that there is another spectral sequence which converges to ...
متن کاملOn Composite Twisted Unknots
Following Mathieu [Ma], Motegi [Mo] and others, we consider the class of possible composite twisted unknots as well as pairs of composite knots related by twisting. At most one composite knot can arise from a particular V -twisting of an unknot; moreover a twisting of the unknot cannot be composite if we have applied more than a single full twist. A pair of composite knots can be related throug...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1254855-x