منابع مشابه
Random Heegaard splittings
Consider a random walk on the mapping class group, and let wn be the location of the random walk at time n. A random Heegaard splitting M(wn) is a 3-manifold obtained by using wn as the gluing map between two handlebodies. We show that the joint distribution of (wn, w −1 n ) is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by th...
متن کاملDistances of Heegaard splittings
J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V ⊂ PML(S). Here h is a pseudo-Anosov homeomorphism of a surface S while V is the set of isotopy classes of simple closed curves in S bounding essential disks in a fixed handlebody. With the same hypothesis we sh...
متن کاملStabilization of Heegaard Splittings
For each g ≥ 2 there is a 3-manifold with two genus g Heegaard splittings that require g stabilizations to become equivalent. Previously known examples required at most one stabilization. Control of families of Heegaard surfaces is obtained through a deformation to
متن کاملSurface Bundles versus Heegaard Splittings
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard splitting. As a consequence, if a splitting surface has small genus compared to...
متن کاملFlipping and Stabilizing Heegaard Splittings
We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thurston of a similar theorem, but with an explicit bound in terms of distance. We also show that in a 3-manifo...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1997
ISSN: 0026-2285
DOI: 10.1307/mmj/1029005621