Covering a nontaming knot by the unlink

Michael H. Freedman; David Gabai

doi:10.2140/agt.2007.7.1561

Covering a nontaming knot by the unlink

Michael H. Freedman
, David Gabai

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

There exists an open 3 -manifold M and a simple closed curve Y M such that π ₁ (M\Y) is infinitely generated, π1(M) is finitely generated and the preimage of Y in the universal covering of M is equivalent to the standard locally finite set of vertical lines in R ³, that is, the trivial link of infinitely many components in R ³.

Original language	English (US)
Pages (from-to)	1561-1578
Number of pages	18
Journal	Algebraic and Geometric Topology
Volume	7
Issue number	1
DOIs	https://doi.org/10.2140/agt.2007.7.1561
State	Published - 2007

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Marden conjecture
Nontaming knot
Tameness

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10.2140/agt.2007.7.1561

Cite this

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title = "Covering a nontaming knot by the unlink",

abstract = "There exists an open 3 -manifold M and a simple closed curve Y M such that π 1 (M\textbackslash{}Y) is infinitely generated, π1(M) is finitely generated and the preimage of Y in the universal covering of M is equivalent to the standard locally finite set of vertical lines in R 3, that is, the trivial link of infinitely many components in R 3.",

keywords = "Marden conjecture, Nontaming knot, Tameness",

author = "Freedman, \{Michael H.\} and David Gabai",

year = "2007",

doi = "10.2140/agt.2007.7.1561",

language = "English (US)",

volume = "7",

pages = "1561--1578",

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T1 - Covering a nontaming knot by the unlink

AU - Freedman, Michael H.

AU - Gabai, David

PY - 2007

Y1 - 2007

N2 - There exists an open 3 -manifold M and a simple closed curve Y M such that π 1 (M\Y) is infinitely generated, π1(M) is finitely generated and the preimage of Y in the universal covering of M is equivalent to the standard locally finite set of vertical lines in R 3, that is, the trivial link of infinitely many components in R 3.

AB - There exists an open 3 -manifold M and a simple closed curve Y M such that π 1 (M\Y) is infinitely generated, π1(M) is finitely generated and the preimage of Y in the universal covering of M is equivalent to the standard locally finite set of vertical lines in R 3, that is, the trivial link of infinitely many components in R 3.

KW - Marden conjecture

KW - Nontaming knot

KW - Tameness

UR - https://www.scopus.com/pages/publications/73649138226

UR - https://www.scopus.com/pages/publications/73649138226#tab=citedBy

U2 - 10.2140/agt.2007.7.1561

DO - 10.2140/agt.2007.7.1561

M3 - Article

AN - SCOPUS:73649138226

SN - 1472-2747

VL - 7

SP - 1561

EP - 1578

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

ER -

Covering a nontaming knot by the unlink

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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