Knots with Braid Index Three Have Property-P
نویسندگان
چکیده
منابع مشابه
Knots with Braid Index Three Have Property-p
We prove that knots with braid index three in the 3-sphere satisfy the Property P conjecture.
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We calculate the alternation number of torus knots with braid index 4 and less. For the lower bound, we use the Upsilon-invariant recently introduced by Ozsváth, Stipsicz, and Szabó. For the upper bound, we use a known bound for braid index 3 and a new bound for braid index 4. Both bounds coincide, so that we obtain a sharp result.
متن کاملA PROJECTIVE PLANE IN Iw4 WITH THREE CRITICAL POINTS IS STANDARD. STRONGLY INVERTIBLE KNOTS HAVE PROPERTY P
LET P be the projective plane in [w4 obtained by capping off the boundary of an unknotted Miibius band in Iw3 x (0) with an unknotted disk in Iw3 x [O, co). Here we show that any smoothly imbedded projective plane in [w4 on which some projection Iw4+lR has three nondegenerate critical points is isotopic to P. The proof is based on a combinatorial solution to Problem 1.2B of [4]. In particular, ...
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We survey two of the many aspects of the standard braid order, namely its set theoretical roots, and the known connections with knot theory, including results by Netsvetaev, Malyutin, and Ito, and very recent work in progress by Fromentin and Gebhardt. It has been known since 1992 [7, 8] that Artin’s braid groups Bn are leftorderable, by an ordering that has several remarkable properties. In pa...
متن کاملProperty P for Knots admitting Certain Gabai Disks
We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then this knot has Property P. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Property P. Other applications are given.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2003
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216503002457