相关论文: Satellite Links with Multiple Full Twists and Sing…
A positive braid with at least one full twist is known to be a minimal braid, i.e, it achieves the braid index for its closure. In this paper we find knots that are the closure of positive minimal braids that cannot be represented by…
A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully…
For an oriented surface link $S$, we can take a satellite construction called a 2-dimensional braid over $S$, which is a surface link in the form of a covering over $S$. We demonstrate that 2-dimensional braids over surface links are useful…
We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently…
A geometric braid $B$ can be interpreted as a loop in the space of monic complex polynomials with distinct roots. This loop defines a function $g:\mathbb{C}\times S^1\to\mathbb{C}$ that vanishes on $B$. We define the set of P-fibered braids…
A Lorenz link is equivalent to a T-link, which is a positive braid built by concatenating torus braids of increasing size. When each torus braid except the largest is obtained by full twists, then the T-link can be described as the Dehn…
We construct infinitely many families of Lorenz knots that are satellites but not cables, giving counterexamples to a conjecture attributed to Morton. We amend the conjecture to state that Lorenz knots that are satellite have companion a…
Twisted links are obtained from a base link by starting with a $n$-braid representation, choosing several ($m$) adjacent strands, and applying one or more twists to the set. Various restrictions may be applied, e.g. the twists may be…
Lorenz links and T-links are equivalent families by the work of Birman--Kofman. Lorenz links arise as periodic orbits of the Lorenz system, whereas T-links are closures of certain positive braids. Birman, Williams, and Franks showed that…
We prove that the property of admitting no cosmetic crossing changes is preserved under the operation of forming certain satellites of winding number zero. We also define strongly cosmetic crossing changes and we discuss their behavior…
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this…
We show that every non-trivial strongly quasipositive link is smoothly concordant to infinitely many pairwise non-isotopic strongly quasipositive links. In contrast to our result, Baker conjectured that smoothly concordant strongly…
We prove that satellite operations that satisfy a certain positivity condition and have winding number other than one are not homomorphisms. The argument uses the $d$-invariants of branched covers. In the process, we prove a technical…
We study a subset of square free positive braids and we give a few algebraic characterizations of them and one geometric characterization: the set of positive braids whose closures are unlinks. We describe canonical forms of these braids…
We begin the systematic study of knot polynomials for the twist satellites of a knot, when its strand is substituted by a 2-strand twist knot. This is a generalization of cabling (torus satellites), when the substitute of the strand was a…
In this paper, we show that the Gluck twist of certain satellite $2$-knots in a $4$-manifold do not change the diffeomorphism type in three different ways: one is directly from the definition of the satellite $2$-knot, and the other two are…
In a recent work "Arc-presentation of links: Monotonic simplification" Ivan Dynnikov showed that each rectangular diagram of the unknot, composite link, or split link can be monotonically simplified into a trivial, composite, or split…
We provide a characterization for multitwists satisfying the braid relation in the mapping class group of an orientable surface.
We give some conditions on positive braids with at least two full twists that ensure their closure is a hyperbolic knot, with applications to the geometric classification of T-links, arising from dynamics, and twisted torus knots.
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T--links are a natural generalization, given by repeated positive twisting. We establish a one-to-one correspondence between…