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Proceedings of the American Mathematical Society

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A normal form in the homeotopy group of a surface of genus $ 2$, with applications to $ 3$-manifolds


Author: Joan S. Birman
Journal: Proc. Amer. Math. Soc. 34 (1972), 379-384
MSC: Primary 57A05
DOI: https://doi.org/10.1090/S0002-9939-1972-0295308-X
MathSciNet review: 0295308
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Abstract: 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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0295308-X
Keywords: Mapping class group, homeotopy group, braid group, Heegaard splitting, closed compact orientable surface
Article copyright: © Copyright 1972 American Mathematical Society