Twist-Roll Spun Knots
نویسندگان
چکیده
منابع مشابه
On the Reversibility of Twist-spun Knots
Litherland has shown that if a knot is (+)-amphicheiral then its m-twist-spin is reversible. We show that, for classical knots, in many cases the converse holds. The irreversibility (sometimes called noninvertibility) of certain twist-spun knots has been established by Ruberman [10], using the Farber-Levine linking pairing and the Casson-Gordon invariants. More recently, alternative proofs of t...
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We investigate which simple even-dimensional knots with finite knot modules may arise as twist-spun simple knots; and give some examples of knots which cannot so arise for reasons which are essentially number-theoretic.
متن کاملTwisting 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.
متن کاملThere are two 2–twist-spun trefoils
We give a short proof inspired by Carter et al [1] that the 2–twist-spun trefoil is not isotopic to its orientation reverse. The proof uses a computer calculation of the third homology group of the three colour rack. We also give a new proof using the same calculation of the well-known fact that the left and right trefoil knots are not isotopic. AMS Classification 57Q45; 57M25, 57M27
متن کاملLegendrian and Transverse Twist Knots
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m(52) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston–Bennequin number of the twist knot K−2n with crossing number 2n+1. In this paper we give a complete classification of Legendrian and transverse representatives o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.2307/2161054