Twisting spun 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.
متن کاملOn 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.
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Smooth time dependent supergravity solutions corresponding to analytic continuations of Kerr black holes are constructed and limits with a local de Sitter phase are found. These solutions are non-singular due to a helical twist in space and a fine tuning of the energy flow in the spacetime. For the extremal limit in which the mass and twist parameters are equal the S-brane undergoes de Sitter e...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1965
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1965-0195085-8