A new proof of the Reidemeister-Singer theorem on stable equivalence of Heegaard splittings

Source abstract

A proof of the Reidemeister-Singer theorem on stable equivalence of Heegaard splittings is given. This proof makes use of the Chillingworth theorem on the preservation of simplicial collapses for subdivisions of complexes of dimension less than or equal to three, and it is based on the observation that subdivision and collapsing preserve stable equivalence.