Knot conjecture

Author: pxae

August undefined, 2024

WebCurrently, 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. 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 …

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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... WebConjecture 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. iphone teams 写真添付

Property P conjecture - Wikipedia

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. 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. 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 … orange long sleeve shirt walmart

Witten’s conjecture and Property P - Harvard University

(PDF) On pretzel knots and Conjecture ℤ - ResearchGate

Webstate polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has Webprojecteuclid.org orange long sleeve shirt toddlerWeba 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 … iphone teams 会議開催

"WebA 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 ... " - Knot conjecture

Knot conjecture

A cabling conjecture for knots in lens spaces SpringerLink

WebIn mathematics, the Property P conjecture is a statement about 3-manifolds obtained by Dehn surgery on a knot in the 3-sphere. A knot in the 3-sphere is said to have Property P if every 3-manifold obtained by performing (non-trivial) … 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 ...

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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 … 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. ...

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 … 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 …

WebGCD(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- 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.

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 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... iphone teams app share screenWebConjecture in knot theory In the branch of mathematicscalled knot theory, the volume conjectureis the following open problem that relates quantum invariantsof knots to the … iphone teams 画面共有横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 … iphone teams 画面共有乱れる