High-codimensional knots spun about manifolds
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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For a fixed isotopy type K of unframed knots in S there are infinitely many isotopy classes of framed knots that correspond to K when we forget the framing. We show that the same fact is true for all the isotopy types of unframed knots in a closed oriented 3-manifold M , provided that M 6= (S × S)#M . On the other hand for any M = (S × S)#M ′ we construct examples of isotopy classes of unframed...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2007
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2007.7.359