عقدة شريحة
العقدة الشريحة slice knot، هي نوع من العقد الرياضية.
تعريفات
In knot theory, a "knot" means an embedded circle in the 3-sphere
and that the 3-sphere can be thought of as the boundary of the four-dimensional ball
A knot is slice if it bounds a nicely embedded 2-dimensional disk D in the 4-ball.
What is meant by "nicely embedded" depends on the context, and there are different terms for different kinds of slice knots. If D is smoothly embedded in B4, then K is said to be smoothly slice. If D is only locally flat (which is weaker), then K is said to be topologically slice.
أمثلة
The following is a list of all slice knots withعشرة or fewer crossings; it was compiled using the Knot Atlas[]: ,, , , , , , , , , , , , , , , , , , and .
الخصائص
Every ribbon knot is smoothly slice. An old question of Fox asks whether every smoothly slice knot is actually a ribbon knot.
The signature of a slice knot is zero.
The Alexander polynomial of a slice knot factors as a product where is some integral Laurent polynomial. This is known as the Fox–Milnor condition.
انظر أيضاً
- Slice genus
- رابط شريحة
المصادر
- ^ Lickorish, W. B. Raymond (1997), An Introduction to Knot Theory, Graduate Texts in Mathematics, 175, Springer, p. 86, ISBN 9780387982540, https://books.google.com/books?id=PhHhw_kRvewC&pg=PA86.
- ^ نطقب:Knot Atlas
- ^ Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail (2010), "Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures", Geometry & Topology 14 (4): 2305–2347, doi:.
- ^ Lickorish (1997), p. 90.
- ^ Banagl, Markus; Vogel, Denis (2010), The Mathematics of Knots: Theory and Application, Contributions in Mathematical and Computational Sciences, 1, Springer, p. 61, ISBN 9783642156373, https://books.google.com/books?id=SavMxpeqSFwC&pg=PA61.
