63 research outputs found
Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links
We consider closed orientable 3-dimensional hyperbolic manifolds which are
cyclic branched coverings of the 3-sphere, with branching set being a
two-bridge knot (or link). We establish two-sided linear bounds depending on
the order of the covering for the Matveev complexity of the covering manifold.
The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and
Gueritaud-Futer (who recently improved previous work of Lackenby), while the
upper estimate is based on an explicit triangulation, which also allows us to
give a bound on the Delzant T-invariant of the fundamental group of the
manifold.Comment: Estimates improved using recent results of Gueritaud-Futer and
Kim-Ki
Generalized Takahashi manifolds
We introduce a family of closed 3-dimensional manifolds, which are a
generalization of certain manifolds studied by M. Takahashi. The manifolds are
represented by Dehn surgery with rational coefficients on the 3-sphere, along
an n-periodic 2n-component link. A presentation of their fundamental group is
obtained, and covering properties of these manifolds are studied. In
particular, this family of manifolds includes the whole class of cyclic
branched coverings of two-bridge knots. As a consequence we obtain a simple
explicit surgery presentation for this important class of manifolds.Comment: 20 pages, 15 figure
Complexity, Heegaard diagrams and generalized Dunwoody manifolds
We deal with Matveev complexity of compact orientable 3-
manifolds represented via Heegaard diagrams. This lead us to the definition
of modified Heegaard complexity of Heegaard diagrams and of
manifolds. We define a class of manifolds which are generalizations of
Dunwoody manifolds, including cyclic branched coverings of two-bridge
knots and links, torus knots, some pretzel knots, and some theta-graphs.
Using modified Heegaard complexity, we obtain upper bounds for their
Matveev complexity, which linearly depend on the order of the covering.
Moreover, using homology arguments due to Matveev and Pervova we
obtain lower bounds
On Hyperbolic with Arbitrary many Singular Components
We construct a family of (n + 1)-component links
which are closures of rational 3-string braids
and show that for n \geq 3 they arise as singular sets of hyperbolic
. Moreover, their 2-fold branched coverings are described
by Dehn surgeries
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