Displaying similar documents to “On tame embeddings of solenoids into 3-space”

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.

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...

Homogeneity of dynamically defined wild knots.

Gabriela Hinojosa, Alberto Verjovsky (2006)

Revista Matemática Complutense

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In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.

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.