A note on untwisted deform-spun $2$-knots
نویسندگان
چکیده
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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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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Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of S n. We show that all frame-spun knots are slice (null-cobordant).
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1992
ISSN: 0386-2194
DOI: 10.3792/pjaa.68.75