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Heegaard genera in
congruence towers of hyperbolic 3-manifolds
BoGwang Jeon |
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Vol. 258 (2012), No. 1, 143–164
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Abstract |
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Given a closed hyperbolic 3-manifold M, we construct a tower of covers with increasing Heegaard genus and give an explicit lower bound on the Heegaard genus of such covers as a function of their degree. Using similar methods, we prove that for any 𝜖 > 0 there exist infinitely many congruence covers {Mi} such that, for any x ∈ M, Mi contains an embedded ball Bx (with center x) satisfying vol Bx > (vol Mi)1∕4−𝜖. We get similar results for an arithmetic noncompact case. |
Keywords
Heegaard genus, hyperbolic 3-manifold, congruence cover
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Mathematical Subject Classification 2010
Primary: 57M10, 57M27
Secondary: 11R04
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Milestones
Received: 31 July 2011
Accepted: 26 April 2012
Published: 21 July 2012
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Authors |
| BoGwang Jeon | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801 United States |
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