Displaying similar documents to “Uncountably many wild knots whose cyclic branched covering are S3.”

Open 3-manifolds, wild subsets of S and branched coverings.

José María Montesinos-Amilibia (2003)

Revista Matemática Complutense

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In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S --> S branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while...

Cyclic branched coverings of 2-bridge knots.

Alberto Cavicchioli, Beatrice Ruini, Fulvia Spaggiari (1999)

Revista Matemática Complutense

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In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.

Representing open 3-manifolds as 3-fold branched coverings.

José María Montesinos-Amilibia (2002)

Revista Matemática Complutense

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It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S, and in some cases, a 2-fold branched covering of S. The branching set is a locally finite disjoint union of strings.

θ -curves inducing two different knots with the same 2 -fold branched covering spaces

Soo Hwan Kim, Yangkok Kim (2003)

Bollettino dell'Unione Matematica Italiana

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For a knot K with a strong inversion i induced by an unknotting tunnel, we have a double covering projection Π : S 3 → S 3 / i branched over a trivial knot Π ⁢ fix ⁢ i , where fix ⁢ i is the axis of i . Then a set Π ⁢ fix ⁢ i ∪ K is called a θ -curve. We construct θ -curves and the Z 2 ⊕ Z 2 cyclic branched coverings over θ -curves, having two non-isotopic Heegaard decompositions which are one stable equivalent.