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Representing 3-manifolds by a universal branching set

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Montesinos Amilibia, José María (1983) Representing 3-manifolds by a universal branching set. Mathematical Proceedings of the Cambridge Philosophical Society, 94 (1). pp. 109-123. ISSN 0305-0041

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Official URL: http://journals.cambridge.org/abstract_S0305004100060941


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Abstract

The author shows that every compact connected oriented 3-manifold, after capping off boundary components by cones, is a covering of S3 branched over the 1-complex G which is "a pair of eyeglasses''. The author gives algorithms for passing between a Heegaard decomposition of a 3-manifold and this covering description. He also determines necessary and sufficient conditions for such a covering to have cone singularities. In a paper by W. Thurston ["Universal links'', Preprint], a link with similar properties (for closed 3-manifolds) to G is constructed.


Item Type:Article
Uncontrolled Keywords:branched coverings of the 3-sphere; finite presentation of fundamental group; compact, connected, oriented 3-manifold without 2-spheres in the boundary; singular 3-manifold; Heegaard diagram
Subjects:Sciences > Mathematics > Topology
ID Code:17198
Deposited On:26 Nov 2012 09:14
Last Modified:12 Dec 2018 15:14

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