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The exterior of a knot K is the complement of an open solid torus knotted like K. The removed open solid torus is called a tubular neighborhood (Adams 1994, p. 258).

The least genus of any Seifert surface for a given knot. The unknot is the only knot with genus 0. Usually, one denotes by g(K) the genus of the knot K. The knot genus has ...

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

An operation on a knot or link diagram which preserves its crossing number. Thistlethwaite used 13 different moves in generating a list of 16-crossing alternating knots ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

A knot diagram which does not specify whether crossings are under- or overcrossings.

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...