. G T ] 5 O ct 2 00 3 ALMOST NORMAL HEEGAARD SURFACES
نویسنده
چکیده
We present a new and shorter proof of Stocking's result that any strongly irreducible Heegaard surface of a closed orientable triangulated 3– manifold is isotopic to an almost normal surface. We also reprove a result of Jaco and Rubinstein on normal spheres. Both proofs are based on the " reduction " technique introduced by the author.
منابع مشابه
M ar 2 00 3 ALMOST NORMAL HEEGAARD SURFACES
We present a new and shorter proof of Stocking's result that any strongly irreducible Heegaard surface of a closed orientable triangulated 3– manifold is isotopic to an almost normal surface. We also reprove a result of Jaco and Rubinstein on normal spheres.
متن کاملar X iv : m at h / 03 03 37 7 v 2 [ m at h . G T ] 1 3 Ju n 20 03 ALMOST NORMAL HEEGAARD SURFACES
We present a new and shorter proof of Stocking's result that any strongly irreducible Heegaard surface of a closed orientable triangulated 3– manifold is isotopic to an almost normal surface. To make our paper essentially self-contained, we reprove a result of Jaco and Rubinstein on normal spheres, Scharlemann's " no nesting " lemma, and the fact that S 3 has no strongly irre-ducible Heegaard s...
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The general scheme that one would like to follow to prove Theorem 1 is to search for bridge punctured 2-spheres by arranging for them to sit in normal or almost normal form with respect to some triangulation of M. There are a number of technical obstructions to this, however, and so this scheme must be adapted as follows. Firstly, bridge punctured 2-spheres are, much like Heegaard surfaces, hig...
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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 Assuming an unpublished result of Pitts and Rubinstein improves this to g ≥ 1 2 cosh(r) + 1 2 .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...
متن کامل2 7 O ct 2 00 4 ON THE HEEGAARD FLOER HOMOLOGY OF S 3 − p / q ( K )
Assume that the oriented 3-manifold M = S 3 −p/q (K) is obtained by a rational surgery (with coefficient −p/q < 0) along an algebraic knot K ⊂ S 3. We compute the Heegaard Floer homology of −M in terms of p/q and the Alexander polynomial of K.
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تاریخ انتشار 2003