Heegaard genus and property τ for hyperbolic 3-manifolds
نویسندگان
چکیده
We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ . As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.
منابع مشابه
S ep 2 00 5 HEEGAARD SPLITTINGS , THE VIRTUALLY HAKEN CONJECTURE AND PROPERTY ( τ ) MARC LACKENBY
The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have profound ramifications for 3-manifold theory. In this paper,...
متن کاملS ep 2 00 2 HEEGAARD SPLITTINGS , THE VIRTUALLY HAKEN CONJECTURE AND PROPERTY ( τ )
The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have many ramifications for 3-manifold theory. In this paper, we ...
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The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have many ramifications for 3-manifold theory. In this paper, we ...
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The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have profound ramifications for 3-manifold theory. In this paper,...
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