The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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.