Displaying similar documents to “Notes on tiled incompressible tori”

An unknotting theorem for tori in 4-dimensional spheres.

Akiko Shima (1998)

Revista Matemática Complutense

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Let T be a torus in S4 and T* a projection of T. If the singular set Gamma(T*) consists of one disjoint simple closed curve, then T can be moved to the standard position by an ambient isotopy of S4.

Essential tori admitting a standard tiling

Leonid Plachta (2006)

Fundamenta Mathematicae

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Birman and Menasco (1994) introduced and studied a class of embedded tori in closed braid complements which admit a standard tiling. The geometric description of the tori from this class was not complete. Ng showed (1988) that each essential torus in a closed braid complement which admits a standard tiling possesses a staircase tiling pattern. In this paper, we introduce and study the so-called longitude-meridional patterns for essential tori admitting a standard...

Some examples of essential laminations in 3-manifolds

Allen Hatcher (1992)

Annales de l'institut Fourier

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Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.

Tangle decompositions of satellite knots.

Chuichiro Hayashi, Hiroshi Matsuda, Makoto Ozawa (1999)

Revista Matemática Complutense

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We study when an essential tangle decomposition of a satellite knot gives an essential tangle decomposition of the companion knot, that is, when the decomposing sphere can be isotoped to intersect the knotted solid torus identified with the pattern in meridian disks.