Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal
نویسندگان
چکیده
منابع مشابه
Horizontal Heegaard Splittings of Seifert Fibered Spaces
We show that if an orientable Seifert fibered space M with an orientable genus g base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of Z. The correspondence is determined by the slopes of intersection of each Heegaard splitting with a collecti...
متن کاملThe Irreducibility of Heegaard Splittings of Seifert Fibered Spaces
Moriah and Schultens have demonstrated that an irreducible Heegaard splitting of an orientable Seifert fibered space over an orientable base surface is either vertical or horizontal. In this paper it is determined precisely which vertical and horizontal splittings are irreducible. Let M be a Seifert fibered space which admits a horizontal splitting at the fiber f . If the genus of the horizonta...
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The infimal Heegaard gradient of a 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3manifolds, and show that a compact orientable Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it virtually fibers over the circle or over a surface other than the...
متن کاملLocal detection of strongly irreducible Heegaard splittings
Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible.
متن کاملSurface Bundles with Genus Two Heegaard Splittings
It is known that there are surface bundles of arbitrarily high genus which have genus two Heegaard splittings. The simplest examples are Seifert fibered spaces with the sphere as a base space, three exceptional fibers and which allow horizontal surfaces. We characterize the monodromy maps of all surface bundles with genus two Heegaard splittings and show that each is the result of integral Dehn...
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ژورنال
عنوان ژورنال: Topology
سال: 1998
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(97)00072-4