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2004 Large embedded balls and Heegaard genus in negative curvature
David Bachman, Daryl Cooper, Matthew E White
Algebr. Geom. Topol. 4(1): 31-47 (2004). DOI: 10.2140/agt.2004.4.31

Abstract

We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g12 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g12 cosh(r)+12. We also give an upper bound on the volume in terms of the flip distance of a Heegaard splitting, and describe isoperimetric surfaces in hyperbolic balls.

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David Bachman. Daryl Cooper. Matthew E White. "Large embedded balls and Heegaard genus in negative curvature." Algebr. Geom. Topol. 4 (1) 31 - 47, 2004. https://doi.org/10.2140/agt.2004.4.31

Information

Received: 30 May 2003; Revised: 21 August 2003; Accepted: 29 August 2003; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1056.57014
MathSciNet: MR2031911
Digital Object Identifier: 10.2140/agt.2004.4.31

Subjects:
Primary: 57M50
Secondary: 57M27, 57N16

Rights: Copyright © 2004 Mathematical Sciences Publishers

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