Knot conjecture

Author: sguh

August undefined, 2024

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 … WebA knot diagram is alternating if the crossings alternate over, under, over, under, etc. as one travels along the knot. A knot is alternating if it has an alternating diagram. Alternating …

Why is the volume conjecture important? - MathOverflow

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. WebDec 6, 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... rivers near bakersfield ca

Volume conjecture - Wikipedia

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 1, 2024 · Knot theorists proved the validity of a mathematical formula about knots after using machine learning to guess what the formula should be. ... Whether Williamson’s … Webknot complement. 0Motivation Throughout this talk, we will take K to be a knot in the three-sphere S3 = R3 [f¥g. We consider the non-compact three-manifold S3 nK and refer to it as the knot complement. It is known from the work of Gordon and Luecke that the topology of the knot complement completely determines the knot up to a homeomorphism of ... smokey and the bandit 2 semi

A cabling conjecture for knots in lens spaces SpringerLink

Tait

WebJan 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 … 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 … rivers near estes park coloradoWebViewed 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. rivers near longmont co

"" - Knot conjecture

Knot conjecture

WebKNOT 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. ... WebA 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 ...

Did you know?

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... WebThe 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 …

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 … 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 ...

WebAug 5, 2014 · The knots \(K_{r,s}^{p,q}\) are analogous to Berge’s doubly primitive knots of families VII and VIII, the knots lying in the fiber of a trefoil or the figure eight knot (see also … 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 ...

WebIn the mathematical field of topology, knot theory is the study of mathematical knots.While inspired by knots which appear in daily life, such as those in shoelaces and rope, a …

WebDec 6, 2024 · The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new … rivers netball club macksvilleWebMar 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 … rivers near omaha neWebConjecture 1.6 ([Abe16 ]). If K and K0have di eomorphic 0-traces then, up to reversing the orientation of either knot, they are smoothly concordant. The techniques of annulus twisting (see [ Oso06 ], [AJOT13 ]) can be used to produce pairs of knots which share a 0-trace. rivers near palestine ohioWebThe first three of these are related to knot theory, while the fourth makes use of differential geometry. We will also study Seifert fibrations and enumerate the eight 3-dimensional geometries. One goal is to understand the importance of Thurston's geometrization conjecture for the classification of 3-manifolds. rivers near tallahassee flWebA widely open conjecture says that a closed aspherical manifold does not admit a PSC metric. I will show that the connected sum of a closed manifold and some exotic aspherical manifolds carries no PSC metric. The enlargeable length-structure and some of Prof. Tom Farrell and his coauthors' work will be used in the talk. ... such as a knot ... rivers near knoxville tnWebKnot. 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 ... rivers near eureka caWeb2nd 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. rivers near orlando fl