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...
متن کاملWhich Finite Simple Knots Are Twist-spun?
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 کاملOn iterated torus knots and transversal knots
A knot type is exchange reducible if an arbitrary closed n{braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) by a nite sequence of braid isotopies, exchange moves and {destabilizations. (See Figure 1). In the manuscript [6] a transversal knot in the standard contact structure for S3 is de ned to be transversally simple if it is characterized up to trans...
متن کاملTransversal Torus Knots
We classify positive transversal torus knots in tight contact structures up to transversal isotopy.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0288752-8