An alternative proof of Lickorish–Wallace theorem

Abstract

We introduce the concept of s-distance of an unstabilized Heegaard splitting. We prove if a 3-manifold admits an unstabilized genus g Heegaard splitting with s-distance m, then surgery on some (m − 1) components link may produce a 3-manifold which admits a stabilized genus g Heegaard splitting. We also give an alternative proof of the fundamental theorem of surgery theory, which states that every closed orientable 3-manifold is obtained by surgery on some link in 3-sphere.