
Cyclic surgery theorem

In three-dimensional topology, a branch of mathematics, the cyclic surgery theorem states that, for a compact, connected, orientable, irreducible three-manifold "M" whose boundary is a torus "T", if "M" is not a Seifert-fibered space and "r,s" are slopes on "T" such that their Dehn fillings have cyclic fundamental group, then the distance between "r" and "s" (the minimal number of times that two simple closed curves in "T" representing "r" and "s" must intersect) is at most 1. Consequently, there are at most three Dehn fillings of "M" with cyclic fundamental group. The theorem appeared in a 1987 paper written by Marc Culler, Cameron Gordon, John Luecke and Peter Shalen.