Large embedded balls and Heegaard genus in negative curvature
نویسندگان
چکیده
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 Assuming an unpublished result of Pitts and Rubinstein improves this to g ≥ 1 2 cosh(r) + 1 2 .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. AMS Classification 57M50; 57M27, 57N16
منابع مشابه
0 M ay 2 00 3 LARGE EMBEDDED BALLS AND HEEGAARD GENUS IN NEGATIVE
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 Assuming an unpublished result of Pitts and Rubinstein improves this to g ≥ 1 2 cosh(r) + 1 2 .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 isoperim...
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