AbstractThe Morton–Franks–Williams inequality for a link gives a lower bound for the braid index in terms of the HOMFLY polynomial. Franks and Williams conjectured that for any closed positive braid the lower bound coincides with the braid index. In this paper, we show that the bound is achieved for a certain class of closed positive braids. We also give an infinite family of prime closed positive braids such that the lower bound does not coincide with their braid indices
In a previous paper ([14]), the author was able to show that the volumes of certain hyperbolic semi-...
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented k...
For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
In knot theory, a knot may have an invariant which is easily computed but difficult to understand ge...
A long-standing problem in knot theory concerns the additivity of crossing numbers of links under th...
We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive...
For a closed n–braid with a full positive twist and with ` negative crossings, 0 ≤ ` ≤ n, we determ...
We use Ozsvath, Stipsicz, and Szabo's Upsilon invariant to provide bounds on cobordisms between knot...
Abstract In a recent paper, McMullen showed an inequality between the Thurston norm and the Alexande...
A famous result of Bennequin states that for any braid representative of the unknot the Bennequin nu...
We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quas...
The objects of study in this thesis are knots. More precisely, positive braid knots, which include a...
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of pos...
We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogeni...
In a previous paper ([14]), the author was able to show that the volumes of certain hyperbolic semi-...
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented k...
For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
In knot theory, a knot may have an invariant which is easily computed but difficult to understand ge...
A long-standing problem in knot theory concerns the additivity of crossing numbers of links under th...
We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive...
For a closed n–braid with a full positive twist and with ` negative crossings, 0 ≤ ` ≤ n, we determ...
We use Ozsvath, Stipsicz, and Szabo's Upsilon invariant to provide bounds on cobordisms between knot...
Abstract In a recent paper, McMullen showed an inequality between the Thurston norm and the Alexande...
A famous result of Bennequin states that for any braid representative of the unknot the Bennequin nu...
We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quas...
The objects of study in this thesis are knots. More precisely, positive braid knots, which include a...
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of pos...
We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogeni...
In a previous paper ([14]), the author was able to show that the volumes of certain hyperbolic semi-...
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented k...
For an un-oriented link $K$, let $L(K)$ be the ropelength of $K$. It is known that when $K$ has more...
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