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A 3-manifold with a non-subgroup-separable fundamental group

Published online by Cambridge University Press:  17 April 2009

Saburo Matsumoto
Saburo Matsumoto
Affiliation:
Department of Mathematics, University of Melbourne, Parkville Vic 3052, Australia e-mail: [email protected]
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We examine a 3-manifold Γ whose fundamental group is known to be non-subgroup-separable (non-LERF). We show that this manifold Γ is a graph manifold and that the subgroup known to be non-separable is not geometric. On the other hand, there are incompressible surfaces immersed in the manifold which do not lift to embeddings in any finite-degree covering space. We then prove that these bad incompressible surfaces must have non-empty boundary.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 261 - 279
Copyright
Copyright © Australian Mathematical Society 1997

References

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