Persistently laminar branched surfaces
نویسندگان
چکیده
منابع مشابه
Persistently laminar branched surfaces
We define sink marks for branched complexes and find conditions for them to determine a branched surface structure. These will be used to construct branched surfaces in knot and tangle complements. We will extend Delman’s theorem and prove that a non 2-bridge Montesinos knot K has a persistently laminar branched surface unless it is equivalent to K(1/2q1, 1/q2, 1/q3, −1) for some positive integ...
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We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are standard in the theory of branched surfaces, and a sink disk is a disk branc...
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We show how to build tangles T in a 3-ball with the property that any knot obtained by tangle sum with T has a persistent lamination in its exterior, and therefore has property P. The construction is based on an example of a persistent lamination in the exterior of the twist knot 61, due to Ulrich Oertel. We also show how the construction can be generalized to n-string tangles.
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We give sufficient conditions for an R-covered codimension one foliation F of a closed 3-manifold to be carried by an Rcovered branched surface; that is, a branched surface carrying only foliations with the R-covered property. These conditions can be readily verified for many examples. In cases where the branched surface is generated by disks, the R-covered property is stable for F in the sense...
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Given a foliation F of a closed 3-manifold and a Smale flow φ transverse to F, we associate a “simplest” branched surface with the pair (F, φ), which is unique up to two combinatorial moves. We show that all branched surfaces constructed from F and φ can be obtained from the simplest model by applying a finite sequence of these moves chosen so that each intermediate branched surface also carrie...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2012
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2012.v20.n2.a7