6,753 research outputs found
Stabilizing Heegaard splittings of toroidal 3-manifolds
Let be a separating incompressible torus in a 3-manifold . Assuming
that a genus Heegaard splitting can be positioned nicely with
respect to (e.g. is strongly irreducible), we obtain an upper
bound on the number of stabilizations required for to become
isotopic to a Heegaard splitting which is an amalgamation along . In
particular, if is a canonical torus in the JSJ decomposition of , then
the number of necessary stabilizations is at most . As a corollary, this
establishes an upper bound on the number of stabilizations required for and any Heegaard splitting obtained by a Dehn twist of
along to become isotopic.Comment: 21 pages, 18 figures. Version for publication. Generalization of the
main theorem and minor changes in style and forma
Degeneration of Heegaard genus, a survey
We survey known (and unknown) results about the behavior of Heegaard genus of
3-manifolds constructed via various gluings. The constructions we consider are
(1) gluing together two 3-manifolds with incompressible boundary, (2) gluing
together the boundary components of surface times I, and (3) gluing a
handlebody to the boundary of a 3-manifold. We detail those cases in which it
is known when the Heegaard genus is less than what is expected after gluing.Comment: This is the version published by Geometry & Topology Monographs on 3
December 200
Transportation in McMinnville 100 Years Ago
Our project presents a historical view of transportation and its development in McMinnville in the 1910s, especially in 1912. McMinnville was incorporated as a town in 1876 and became a city in 1882. At the time, people still frequently rode horses (including stagecoaches), and the Yamhill River provided an early artery for pioneer travel and commerce. Then rails expanded in Oregon in the late 1800s and became a popular mode of transportation in the early 20th century. By the 1910s, horses, steamboats, rails, and cars were four major modes of transportation in McMinnville
Stabilization, amalgamation, and curves of intersection of Heegaard splittings
We address a special case of the Stabilization Problem for Heegaard
splittings, establishing an upper bound on the number of stabilizations
required to make a Heegaard splitting of a Haken 3-manifold isotopic to an
amalgamation along an essential surface. As a consequence we show that for any
positive integer there are 3-manifolds containing an essential torus and a
Heegaard splitting such that the torus and splitting surface must intersect in
at least simple closed curves. These give the first examples of lower
bounds on the minimum number of curves of intersection between an essential
surface and a Heegaard surface that are greater than one.Comment: Version for publication. To appear in Algebraic and Geometric
Topolog
Response and optimization of an isolation system with relaxation type damping
Response and optimization of isolation system with relaxation type dampin
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