Gluck twisting roll spun knots
نویسندگان
چکیده
We show that the smooth homotopy 4-sphere obtained by Gluck twisting m-twist n-roll spin of any unknotting number one knot is diffeomorphic to standard 4-sphere, for pair integers (m,n). It follows as a corollary an infinite collection twisted doubles Gompf's order corks are standard.
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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Princess Vera's grave in the Korchevatskii cemetery on the outskirts ofKiev is marked by a metal cross in the Catholic rather than the Russian Orthodox style, befitting her Catholic origins tuberculosis of the knee.'9 In 1929 she was appointed professor ofsurgery at the University ofKiev. This was quite an achievement for a princess. She had started to write her memoirs, which were very fiction...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2022
ISSN: ['1472-2739', '1472-2747']
DOI: https://doi.org/10.2140/agt.2022.22.973