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

Birman, Joan S.

doi:10.1090/S0002-9939-1972-0295308-X

A normal form in the homeotopy group of a surface of genus $2$, with applications to $3$-manifolds
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by Joan S. Birman PDF

Proc. Amer. Math. Soc. 34 (1972), 379-384 Request permission

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.

References

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