Knot conjecture

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August undefined, 2024

WebKnot. Contribute To this Entry ». In mathematics, a knot is defined as a closed, non-self- intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the unknot ). While in common usage, knots can be tied in string and rope such that one or more strands are left open on either side of the ... WebEvery ribbon knot is known to be a slice knot. A famous open problem, posed by Ralph Fox and known as the slice-ribbon conjecture, asks if the converse is true: is every (smoothly) slice knot ribbon? (Lisca 2007) showed that the conjecture is …

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WebIn mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a … Web2nd edit: As far as I know, the slice-ribbon conjecture has no major consequences. As I describe above, it's more of an ''outer-marker'' type of conjecture. It's a measure of how well we understand knotting of 2-dimensional things in 4-dimensional things. 3rd edit: Here is a type of mild consequence that was pointed out to me recently. e scooters ottawa price

Conjecture - Wikipedia

WebDec 23, 2024 · The new conjecture — that these two types of invariants are related — will open up new theorizing in the mathematics of knots, the researchers wrote in Nature. In … Webhave found important applications to hyperbolic geometry, the topology of knot complements, and K-theory. More recently, they appear in relation to physics, in particular in the A-J conjecture. However, calculations of A-polynomials remain relatively di cult. In particular, there are very few in nite families of knots for which A-polynomials ... WebSince any knot group is the homomorphic image of the group of a hyper-bolic knot (see for example [15]), it is suﬃcient to prove the conjecture for hyperbolic knots. The main result of this paper is the following, and is the ﬁrst general result for a large class of hyperbolic knots. Theorem 1.2. Conjecture 1.1 holds for all two-bridge knots. finished live edge wood slabs

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WebDec 1, 2024 · A notable example of a conjectured connection is the volume conjecture 26, which proposes that the hyperbolic volume of a knot (a geometric invariant) should be encoded within the asymptotic ... WebA Berge knot (also called a double primitive knot) is a particular type of knot classiﬁed by John Berge. Conjecture The Berge Conjecture states that the only knots which emit lens space surgeries are the Berge knots. e scooter speed limitWebKNOT THEORY K UNIO M URASUGI (Received 28 Jnnuary 1986) 51. INTRODUCTION AND IMAIN THEOREMS LETL bea ... THEOREM A. (P. G. Tait Conjecture) Two (connected and proper) alternating projections of an alternating link have the same number of double points. THEOREM B. The minimal projection of an alternating link is alternating. ... finished loading

"WebFeb 2, 2024 · The slice-ribbon conjecture concerns two types of knots: slice knots and ribbon knots. Figuring out which knots are slice is “one of the fundamental questions that … " - Knot conjecture

Knot conjecture

WebViewed 3k times 26 The volume conjecture, a formula relating hyperbolic volume of a knot complement with the semiclassical limit of a family of coloured Jones polynomials, is widely considered the biggest open problem in quantum topology. Weba knot K has Property P in their sense, it is sufﬁcient to verify that the 3-manifolds Y obtained by non-trivial Dehn surgeries onK all have non-trivial fundamental group. In [6], it …

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WebIn knot theory, the Milnor conjecture says that the slice genus of the torus knot is It is in a similar vein to the Thom conjecture . It was first proved by gauge theoretic methods by Peter Kronheimer and Tomasz Mrowka. [1] Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant. [2] Webknots has also been veri ed by Ozsv ath and Szab o using Heegaard Floer homology [7], and by Jong via a combinatorial method [4]. Recently, Hirasawa and Mura-sugi showed that the conjecture holds for alternating stable knots [3]. Moreover, in this case they observed that the signature of such knots are zero, and m= 0 in Conjecture 1.

WebDec 22, 2015 · Conjecture Zis a knot theoretical equivalent form of the Kervaire Conjecture. We show that Conjecture Z is true for all the pretzel knots of the form P(p, q, −) where p, q and rare odd... The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conjectures have been solved, the most recent being the Flyping conjecture.

WebA knot K is slice if and only if there is a ribbon knot R such that the connected sum K # R is ribbon. One may wish that one didn't have to stabilize. Consider the monoid M of oriented … WebAug 16, 2024 · The volume conjecture states that this function would grow exponentially with respect to N and its growth rate would give the simplicial volume of the knot complement. In this section we describe the volume conjecture and give proofs for the figure-eight knot and for the torus knot T (2, 2 a + 1). Download chapter PDF.

WebMar 24, 2024 · 1. Reduced alternating diagrams have minimal link crossing number, 2. Any two reduced alternating diagrams of a given knot have equal writhe , 3. The flyping …

WebApr 20, 2024 · One of the most venerable tests in knot theory is the Alexander polynomial — a polynomial expression that’s based on the way a given knot crosses over itself. It’s a highly effective test, but it’s also slightly ambiguous. The same knot could yield multiple different (but very closely related) Alexander polynomials. finished livestockWebDec 23, 2024 · The new conjecture — that these two types of invariants are related — will open up new theorizing in the mathematics of knots, the researchers wrote in Nature. In the second case, DeepMind took... e scooters sit downWebGCD(m,n) components; in particular, THK(m,n) is a knot precisely when m and n are relatively prime. If m = 2 and n is odd, THK(2,n) is a (2,n) torus knot and is also a rational knot and a Montessinos knot. The Harary-Kauﬀman Conjecture is known to hold for such knots [KL, APS]. So, we will assume that m is at least 3. Our key obser- finished loading offsets and group metadataWebApr 23, 2024 · The set of knots modulo this relation forms an abelian group with the connect sum operation. This group is called the concordance group of knots in S3 and is denoted … e scooter statisticsWebCurrently, the only knots known to admit hidden symmetries are the ﬁgure-8 and the two dodecahedral knots of Aitchison and Rubinstein described in [1] (c.f. Conjecture 1.3 below). These three knots have cusp ﬁeld Q[√ −3]. There is one known example of a knot with cusp ﬁeld Q[i], and it does not admit hidden symmetries. e scooters surreyWebA few major discoveries in the late 20th century greatly rejuvenated knot theory and brought it further into the mainstream. In the late 1970s William Thurston 's hyperbolization theorem introduced the theory of hyperbolic 3-manifolds into knot theory and made it of prime importance. In 1982, Thurston received a Fields Medal, the highest honor ... finished living shedsWebJan 31, 2010 · The Volume Conjecture states that a certain limit of the colored Jones polynomial of a knot would give the volume of its complement. If we deform the parameter of the colored Jones polynomial we also conjecture that it would also give the volume and the Chern-Simons invariant of a three-manifold obtained by Dehn surgery determined by … finished loading plugins