van Kampen lemma
= van Kampen lemma
{c}
A closed combinatorial path in a <2-complex> is <null-homotopic> exactly when it is the boundary path of a <disc diagram> over that complex. A finite cellular null-homotopy can be arranged into such a planar diagram; conversely the contractible diagram supplies a null-homotopy. In a <group presentation>, this is the geometric form of expressing a trivial word as a product of conjugates of <relators>.