A new proof of the Reidemeister-Singer theorem on stable equivalence of Heegaard splittings
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- by Robert Craggs PDF
- Proc. Amer. Math. Soc. 57 (1976), 143-147 Request permission
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.References
- D. R. J. Chillingworth, Collapsing three-dimensional convex polyhedra, Proc. Cambridge Philos. Soc. 63 (1967), 353–357. MR 210100, DOI 10.1017/s0305004100041268 R. Craggs, Relating representations for $3$-and $4$-manifolds (mimeographed manuscript). K. Reidemeister, Zur dreidimensionalen Topologie, Abh. Math. Sem. Univ. Hamburg 9 (1933), 189-194.
- James Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc. 35 (1933), no. 1, 88–111. MR 1501673, DOI 10.1090/S0002-9947-1933-1501673-5
- Friedhelm Waldhausen, Heegaard-Zerlegungen der $3$-Sphäre, Topology 7 (1968), 195–203 (German). MR 227992, DOI 10.1016/0040-9383(68)90027-X E. C. Zeeman, Seminar on combinatorial topology, Publ. Hautes Études Sci., Paris, 1963 (mimeographed notes).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 143-147
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0410749-9
- MathSciNet review: 0410749