Large embedded balls and Heegaard genus in negative curvature

David Bachman; Daryl Cooper; Matthew E. White

doi:10.2140/agt.2004.4.31

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Large embedded balls and Heegaard genus in negative curvature

David Bachman·Daryl Cooper·Matthew E. White

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Abstract

We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g >= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g >= 1/2 cosh(r) + 1/2. 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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BibTeX RIS

David Bachman, Daryl Cooper, Matthew E. White. 2004-02-14. Large embedded balls and Heegaard genus in negative curvature. https://doi.org/10.2140/agt.2004.4.31

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