### Impacto

### Downloads

Downloads per month over past year

Montesinos Amilibia, José María
(2010)
*The knot engulfing property of 3-manifolds.*
Atti del Seminario Matematico e Fisico dell' Università di Modena e Reggio Emilia , 57
.
pp. 135-140.
ISSN 1825-1269

## Abstract

The Freudenthal compactification of a 3-manifold M is a compactification M′ such that the end space e(M)=M′∖M is a totally disconnected compact set. The topological uniformization conjecture states that the Freudenthal compactification of the universal covering of a connected, closed 3-manifold is S3 with its end space tamely embedded. A 3-manifold M has the knot engulfing property if every contractible polyhedral simple closed curve in M lies in some polyhedral 3-cell in M. A classical result by Bing (1958) is that the only simply connected closed 3-manifold with the knot engulfing property is S3. The author proves a generalization of Bing's result: A simply connected 3-manifold M has the knot engulfing property if and only if the Freudenthal compactification M′ of M is homeomorphic to S3 with the end space e(M) tamely embedded.

Thus the topological uniformization conjecture can be rephrased as stating that the universal covering of a connected, closed 3-manifold has the knot engulfing property.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | knot engulfing property; Cantor set; compactification; end |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 21744 |

Deposited On: | 07 Jun 2013 16:50 |

Last Modified: | 12 Dec 2018 15:13 |

### Origin of downloads

Repository Staff Only: item control page