Displaying similar documents to “Scaling in a map of the two-torus.”

Notes on tiled incompressible tori

Leonid Plachta (2012)

Open Mathematics

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Let Θ denote the class of essential tori in a closed braid complement which admit a standard tiling in the sense of Birman and Menasco [Birman J.S., Menasco W.W., Special positions for essential tori in link complements, Topology, 1994, 33(3), 525–556]. Moreover, let R denote the class of thin tiled tori in the sense of Ng [Ng K.Y., Essential tori in link complements, J. Knot Theory Ramifications, 1998, 7(2), 205–216]. We define the subclass B ⊂ Θ of typical tiled tori and show that...

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...

Plane curve singularities and carousels

Lê Dung Tráng (2003)

Annales de l’institut Fourier

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In this paper we give a direct and explicit description of the local topological embedding of a plane curve singularity using the Puiseux expansions of its branches in a given set of coordinates.

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.