Add to ORKGThis short note is about three-stranded pretzel knots that have an even number of crossings in one of the strands. We calculate the braid index of such knots and determine which of them are quasipositive. The main tools are the Morton-Franks-Williams inequalities, and Khovanov-Rozansky concordance homomorphisms.Comment: 6 pages, 2 figures. v2: Minor changes. Accepted for publication in Communications in Analysis and Geometry. Comments welcom
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...
We provide explicit formulas for the integer-valued smooth concordance invariant $\upsilon(K) = \Ups...
For a peculiar family of double braid knots there is a remarkable factorization formula for the coef...
We use Ozsvath, Stipsicz, and Szabo's Upsilon invariant to provide bounds on cobordisms between knot...
A braid is called quasipositive if it is a product of conjugates of standard generators of the braid...
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We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pret...
In knot theory, a knot may have an invariant which is easily computed but difficult to understand ge...
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive...
The Slice-Ribbon Conjecture, posed by Fox in 1966, is a long-standing open conjecture that posits th...
Abstract. We provide a partial classification of all 3-strand pretzel knots K = P (p, q, r) with un-...
textIn this paper we explore the slice-ribbon conjecture for some families of pretzel knots. Donalds...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
Classically, the study of knots and links has proceeded topologically looking for features of knotte...
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive...
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...
We provide explicit formulas for the integer-valued smooth concordance invariant $\upsilon(K) = \Ups...
For a peculiar family of double braid knots there is a remarkable factorization formula for the coef...
We use Ozsvath, Stipsicz, and Szabo's Upsilon invariant to provide bounds on cobordisms between knot...
A braid is called quasipositive if it is a product of conjugates of standard generators of the braid...
We show that the number of fundamentally differentm-colorings of a knotK depends only on the m-nulli...
We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pret...
In knot theory, a knot may have an invariant which is easily computed but difficult to understand ge...
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive...
The Slice-Ribbon Conjecture, posed by Fox in 1966, is a long-standing open conjecture that posits th...
Abstract. We provide a partial classification of all 3-strand pretzel knots K = P (p, q, r) with un-...
textIn this paper we explore the slice-ribbon conjecture for some families of pretzel knots. Donalds...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
Classically, the study of knots and links has proceeded topologically looking for features of knotte...
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive...
We talk about how to read the braid index of certain families of alternating knots from a minimal kn...
We provide explicit formulas for the integer-valued smooth concordance invariant $\upsilon(K) = \Ups...
For a peculiar family of double braid knots there is a remarkable factorization formula for the coef...