A Normal Form in the Homeotopy Group of a Surface of Genus 2, with Applications to 3-Manifolds

Joan S. Birman
1972 Proceedings of the American Mathematical Society  
It is shown that elements in the homeotopy group of a closed, compact, orientable 2-manifold of genus 2 can be put into a unique normal form which allows them to be enumerated systematically. As an application, the class of 3-manifolds which admit Heegaard splittings of genus 2 are shown to be denumerable, and a procedure is given for enumerating presentations for their fundamental groups.
doi:10.2307/2038376 fatcat:ca2s635dyzh2bazscoezwnmzc4