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Proceedings of the American Mathematical Society

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


Author: Robert Craggs
Journal: Proc. Amer. Math. Soc. 57 (1976), 143-147
MSC: Primary 57A10
MathSciNet review: 0410749
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0410749-9
Keywords: Heegaard splitting, stable equivalence, collapse, subdivision
Article copyright: © Copyright 1976 American Mathematical Society