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Journal of Topology Advance Access published online on October 25, 2007
Journal of Topology, doi:10.1112/jtopol/jtm010
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© 2007 London Mathematical Society

Heegaard genus and property {tau} for hyperbolic 3-manifolds

D. D. Long

Department of Mathematics, University of California, Santa Barbara, CA 93106, USA long{at}math.ucsb.edu

A. Lubotzky

Department of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel alexlub{at}math.huji.ac.il

A. W. Reid

Department of Mathematics, University of Texas, Austin, TX 78712, USA areid{at}math.utexas.edu


  Abstract

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 {tau}. 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.

Received March 25, 2007.

2000 Mathematics Subject Classification 57M10

D.D. Long and A.W. Reid were supported in part by the NSF and A. Lubotzky was supported in part by the NSF and the US-Israel Bi-National Science Foundation.


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