Slice knot information

A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset...

(2,3)-torus knot. It is also the knot obtained by closing the braid σ13. The trefoil is an alternating knot. However, it is not a slice knot, meaning it...

Communications Engine Slice category, in category theory, a special case of a comma category Slice genus, in knot theory Slice knot, in knot theory Slice sampling...

of Mathematics determining that the Conway knot is not a slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior...

the knot is not a smoothly slice knot, though it is topologically slice (the Kinoshita–Terasaka knot is both). Weisstein, Eric W. "Conway's Knot". mathworld...

classical knot theory, however, and an important topic is the study of slice knots and ribbon knots. A notorious open problem asks whether every slice knot is...

ribbon knot if f | M : M → R {\displaystyle f_{|M}\colon M\to \mathbb {R} } has no interior local maxima. Every ribbon knot is known to be a slice knot. A...

reasoned that it would make no difference how the knot was loosed, so he drew his sword and sliced it in half with a single stroke. In an alternative...

of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied...

structure. Lissajous knot Ribbon knot Satellite knot Slice knot Torus knot Transverse knot Twist knot Virtual knot welded knot Wild knot Borromean rings,...

the Arf invariant of a slice knot vanishes. Kauffman (1987) p.74 Kauffman (1987) pp.75–78 Robertello, Raymond, An Invariant of Knot Corbordism, Communications...

twist knot is also a 2-bridge knot. Of the twist knots, only the unknot and the stevedore knot are slice knots. A twist knot with n {\displaystyle n} half-twists...

In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that K is the...

middle rope is sliced. This allows climbers rappelling down cliff faces to keep most of the rope used for the rappel, by tying the knot at the top, and...

a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial...

Boolean functions (Hao Huang, 2019) Deciding whether the Conway knot is a slice knot (Lisa Piccirillo, 2020) Virtual Haken conjecture (Ian Agol, Daniel...

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot...

mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence...

of the knot K. Slice knots are known to have zero signature. Knot signatures can also be defined in terms of the Alexander module of the knot complement...

boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most...

responsible for introducing several basic phrases to knot theory: the phrases slice knot, ribbon knot, and Seifert circle all appear in print for the first...

In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other...

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies...