منابع مشابه
Knots without Cosmetic Crossings
Let K′ be a knot that admits no cosmetic crossing changes and let C be a prime, non-cable knot. Then any knot that is a satellite of C with winding number zero and pattern K′ admits no cosmetic crossing changes. As a consequence we prove the nugatory crossing conjecture for Whitehead doubles of prime, non-cable knots.
متن کاملCosmetic Crossings of Twisted Knots
We prove that the property of admitting no cosmetic crossing changes is preserved under the operation of inserting full twists in the strings of closed braids and the operation of forming certain satellites of winding number zero. As a consequences of the main results, we prove the nugatory crossing conjecture for twisted fibered braids, for closed 3-braids and for Whitehead doubles of prime no...
متن کاملCosmetic surgeries on genus one knots
Let Y be a closed oriented three-manifold and K be a framed knot in Y . For a rational number r , let Yr(K) be the resulting manifold obtained by Dehn surgery along K with slope r with respect to the given framing. For a knot K in S3 , we will always use the Seifert framing. Two surgeries along K with distinct slopes r and s are called cosmetic if Yr(K) and Ys(K) are homeomorphic. The two surge...
متن کاملCosmetic Crossing Changes of Fibered Knots
We prove that a crossing circle L of a fibered knot K bounds a disc in the complement of K, if and only if there is a crossing change supported on L that doesn’t change the isotopy class of K. We also sow that if a knot K is n-adjacent to a fibered knot K′, for some n > 1, then either the genus of K is larger that of K′ or K is isotopic to K′. This statement, which strengthens a result of [9], ...
متن کاملCosmetic surgeries on knots in S 3
Two Dehn surgeries on a knot are called purely cosmetic, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in S, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery formula for correction terms in Heegaard Floer homology.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2016
ISSN: 0166-8641
DOI: 10.1016/j.topol.2016.04.009