# Open 3-manifolds, wild subsets of S3 and branched coverings.

José María Montesinos-Amilibia

Revista Matemática Complutense (2003)

- Volume: 16, Issue: 2, page 577-600
- ISSN: 1139-1138

## Access Full Article

top## Abstract

top## How to cite

topMontesinos-Amilibia, José María. "Open 3-manifolds, wild subsets of S3 and branched coverings.." Revista Matemática Complutense 16.2 (2003): 577-600. <http://eudml.org/doc/44439>.

@article{Montesinos2003,

abstract = {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 : S3 --> S3 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 the branching set changes and becomes wild. As a consequence every closed, oriented 3-manifold is represented as a 3-fold covering of S3 branched over a wild knot, in plenty of different ways, confirming the versatility of irregular branched coverings. Other collection of examples is obtained by pasting the members of an infinite sequence of two-component strongly-invertible link exteriors. These open 3-manifolds are shown to be 2-fold branched coverings of wild knots in the 3-sphere. Two concrete examples, are studied: the solenoidal manifold, and the Whitehead manifold. Both are 2-fold covering of the euclidean space R3 branched over an uncountable collection of string projections in R3.},

author = {Montesinos-Amilibia, José María},

journal = {Revista Matemática Complutense},

keywords = {Variedades topológicas; 3-variedades; Nudos topológicos; Recubrimientos topológicos; simple branched covering; open 3-manifold; wild knot},

language = {eng},

number = {2},

pages = {577-600},

title = {Open 3-manifolds, wild subsets of S3 and branched coverings.},

url = {http://eudml.org/doc/44439},

volume = {16},

year = {2003},

}

TY - JOUR

AU - Montesinos-Amilibia, José María

TI - Open 3-manifolds, wild subsets of S3 and branched coverings.

JO - Revista Matemática Complutense

PY - 2003

VL - 16

IS - 2

SP - 577

EP - 600

AB - 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 : S3 --> S3 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 the branching set changes and becomes wild. As a consequence every closed, oriented 3-manifold is represented as a 3-fold covering of S3 branched over a wild knot, in plenty of different ways, confirming the versatility of irregular branched coverings. Other collection of examples is obtained by pasting the members of an infinite sequence of two-component strongly-invertible link exteriors. These open 3-manifolds are shown to be 2-fold branched coverings of wild knots in the 3-sphere. Two concrete examples, are studied: the solenoidal manifold, and the Whitehead manifold. Both are 2-fold covering of the euclidean space R3 branched over an uncountable collection of string projections in R3.

LA - eng

KW - Variedades topológicas; 3-variedades; Nudos topológicos; Recubrimientos topológicos; simple branched covering; open 3-manifold; wild knot

UR - http://eudml.org/doc/44439

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.