Is Trefoil a torus knot?
The trefoil can be described as the (2,3)-torus knot. It is also the knot obtained by closing the braid σ13. The trefoil is an alternating knot.
Are torus knots alternating?
-torus knots are almost alternating knots (Adams 1994, p. 142).
What is a twisted torus?
Twisted torus knots are torus knots with some full twists added along some number of adjacent strands. There are infinitely many known examples of twisted torus knots which are actually torus knots.
Is a torus a donut?
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
What is the genus of a triple torus?
genus-3 torus
A sphere with three handles (and three holes), i.e., a genus-3 torus.
Is the cinquefoil knot Tricolorable?
The figure-eight knot is not tricolorable (it requires four colors): Danger: many knots are tricolorable — being tricolorable doesn’t mean that your knot is the trefoil knot — but it does mean that your knot is not the unknot!
What is a flat torus?
Flat tori. A flat torus is a quotient Γ\Rn of Euclidean space Rn by a lattice Γ of full rank. The Laplacian on the torus is the restriction of the Euclidean Laplacian on Rn to the smooth Γ-periodic functions.
What is a 2D torus?
2D Torus: it is two dimension with degree of 4, the nodes are imagined laid out in a two-dimensional rectangular lattice of n rows and n columns, with each node connected to its 4 nearest neighbors, and corresponding nodes on opposite edges connected.
What is a torus knot and torus link?
Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is gcd ( p, q )).
How to find the crossing number of a torus knot?
The crossing number of a ( p, q) torus knot with p, q > 0 is given by c = min ( ( p −1) q, ( q −1) p ). g = 1 2 ( p − 1 ) ( q − 1 ) . {\\displaystyle g= {\\frac {1} {2}} (p-1) (q-1).}
What is a double torus link?
If a link is a subset of a genus two handlebody, it is a double torus link. For genus two, the simplest example of a double torus knot that is not a torus knot is the figure-eight knot. ^ a b cLivingston, Charles (1993). Knot Theory. Mathematical Association of America. p.
What is the number of components of a torus link?
A torus link arises if p and q are not coprime (in which case the number of components is gcd ( p, q )). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot .