A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a link invariant always assigns the same value to equivalent links (although different knots may have the same link invariant). When the link has a single component and therefore generates to a knot, the invariant is called a knot invariant.

# Link Invariant

## See also

Knot, Knot Invariant, Link## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Link Invariant." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/LinkInvariant.html