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Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

The unlink, also called the trivial link, of n components consist of n disjoint circles in a plane (Rolfsen 1976, p. 65).

A single component algebraic link. Most knots up to 11 crossings are algebraic, but they quickly become outnumbered by nonalgebraic knots for more crossings (Hoste et al. ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

A projection of a link is tricolorable if each of the strands in the projection can be colored in one of three different colors such that, at each crossing, all three colors ...

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

A polynomial which is not necessarily an invariant of a link. It is related to the dichroic polynomial. It is defined by the skein relationship ...

A knot property, also called the twist number, defined as the sum of crossings p of a link L, w(L)=sum_(p in C(L))epsilon(p), (1) where epsilon(p) defined to be +/-1 if the ...