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Graph manifolds with non-empty boundary are covered by surface bundles

Published online by Cambridge University Press:  01 November 1997

SHICHENG WANG  and
FENGCHUN YU
SHICHENG WANG
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China
FENGCHUN YU
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, China
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Abstract

A classical fact is that Seifert manifolds with non-empty boundary are covered by surface bundles over the circle S1 and closed Seifert manifolds may or may not be covered by surface bundles over S1. Some closed graph manifolds are not covered by surface bundles over S1 ([LW] and [N]). Thurston asked if complete hyperbolic 3-manifolds of finite volume are covered by surface bundles [T]. J. Luecke and Y. Wu asked if graph manifolds with non-empty boundary are covered by surface bundles over S1 ([LW]). In this paper we prove:

THEOREM 0·1. Each graph manifold with non-empty boundary is finitely covered by a surface bundle over the circle S1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 447 - 455
Copyright
Cambridge Philosophical Society 1997

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