A new proof of the Reidemeister-Singer theorem on stable equivalence of Heegaard splittings-Reference-Cited by-同舟云学术

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

Published:1976 Issue:1 Volume:57 Page:143-147
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Craggs Robert

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1976-057-01/S0002-9939-1976-0410749-9/S0002-9939-1976-0410749-9.pdf

Reference6 articles.

1. Collapsing three-dimensional convex polyhedra;Chillingworth, D. R. J.;Proc. Cambridge Philos. Soc.,1967

2. R. Craggs, Relating representations for 3-and 4-manifolds (mimeographed manuscript).

3. K. Reidemeister, Zur dreidimensionalen Topologie, Abh. Math. Sem. Univ. Hamburg 9 (1933), 189-194.

4. Three-dimensional manifolds and their Heegaard diagrams;Singer, James;Trans. Amer. Math. Soc.,1933

5. Heegaard-Zerlegungen der 3-Sphäre;Waldhausen, Friedhelm;Topology,1968

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