Knot conjecture

Author: fpmi

August undefined, 2024

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 ... WebSimon’s conjecture for two-bridge knots 123 In order to control the image of the longitude, we introduce the fol-lowing deﬁnition which can be thought as a kind of smallness for the …

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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 ... WebNov 12, 2024 · Diagnosis. In most cases, Dupuytren contracture can be diagnosed by the look and feel of the hands. Other tests are rarely necessary. Health care providers … civ knjiga

Why is the volume conjecture important? - MathOverflow

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 … WebAug 5, 2014 · These knots are typically hyperbolic. We also demonstrate that the previously known two families of examples of hyperbolic knots in non-prime manifolds with lens space surgeries of Eudave-Muñoz–Wu and Kang all fit this construction. As such, we propose a generalization of the cabling conjecture of González-Acuña–Short for knots in lens ... 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. civ kupe guide

Conject Definition & Meaning - Merriam-Webster

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 … 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. civ jeuWebprojecteuclid.org civnats

"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. " - Knot conjecture

Knot conjecture

big list - Properties and conjectures about alternating 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... 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.

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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- 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 ...

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 …

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. WebApr 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 …

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 ...

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 … civmec gladstoneWebKNOT 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. ... civljane poštanski brojWebhave 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 ... civ mbo rijnlandWeba 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 … civl service jobs glasgowWebViewed 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. civ kristinaWebCurrently, 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. civ klonWebConjecture 1. Every slice knot is a ribbon knot. A variety of obstructions to a knot being ribbon have been developed, but the conjecture remains open in the general case. … civnat