Editing Linking number (section)

==Generalizations==
[[File:BorromeanRings.svg|thumb|The [[Milnor invariants]] generalize linking number to links with three or more components, allowing one to prove that the [[Borromean rings]] are linked, though any two components have linking number 0.]]
* Just as closed curves can be [[link (knot theory)|linked]] in three dimensions, any two [[closed manifold]]s of dimensions ''m'' and ''n'' may be linked in a [[Euclidean space]] of dimension <math>m + n + 1</math>.  Any such link has an associated Gauss map, whose [[degree of a continuous mapping|degree]] is a generalization of the linking number.
* Any [[framed knot]] has a [[self-linking number]] obtained by computing the linking number of the knot ''C'' with a new curve obtained by slightly moving the points of ''C'' along the framing vectors.  The self-linking number obtained by moving vertically (along the blackboard framing) is known as '''Kauffman's self-linking number'''.
* The linking number is defined for two linked circles; given three or more circles, one can define the [[Milnor invariants]], which are a numerical invariant generalizing linking number.
* In [[algebraic topology]], the [[cup product]] is a far-reaching algebraic generalization of the linking number, with the [[Massey product]]s being the algebraic analogs for the [[Milnor invariants]].
* A [[linkless embedding]] of an [[undirected graph]] is an embedding into three-dimensional space such that every two cycles have zero linking number. The graphs that have a linkless embedding have a [[forbidden graph characterization|forbidden minor characterization]] as the graphs with no [[Petersen family]] [[minor (graph theory)|minor]].