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A torus reduction theorem for regular coverings of 3-manifolds by homology 3-spheres

Published online by Cambridge University Press:  24 October 2008

E. Luft  and
D. Sjerve
E. Luft
Affiliation:
Department of Mathematics, University of British Columbia, 121–1984 Mathematics Road, Vancouver, B.C., Canada, V6T 1Y4
D. Sjerve
Affiliation:
Department of Mathematics, University of British Columbia, 121–1984 Mathematics Road, Vancouver, B.C., Canada, V6T 1Y4
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Abstract

For any regular covering p:M→M of 3-dimensional manifolds M, M with M a homology 3-sphere we construct a regular covering p′: M′ → M′ of 3-manifolds M′, M′ with the same group of covering transformations and a degree 1 map f:M → M′ so that M′ is a homology 3-sphere, M′ (and hence M′) is irreducible and does not contain incompressible tori, and the regular covering p:M→M is induced from the regular covering p′: M′ → M′ by the map f. Assuming Thurston's geometrization conjecture it follows that M′ (and hence M′) is either hyperbolic or Seifert fibred.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 117 - 124
Copyright
Copyright © Cambridge Philosophical Society 1991

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