A characterization of 2-knots groups.

Francisco González-Acuña

Revista Matemática Iberoamericana (1994)

  • Volume: 10, Issue: 2, page 221-228
  • ISSN: 0213-2230

Abstract

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A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sn+2. Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y].We will give here a characterization of 2-knot groups in terms of presentations. It has the flavor of Artin's characterization of 1-knot groups. S. Kamada has independently obtained another characterization of 2-knot groups ([Ka]).

How to cite

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González-Acuña, Francisco. "A characterization of 2-knots groups.." Revista Matemática Iberoamericana 10.2 (1994): 221-228. <http://eudml.org/doc/39454>.

@article{González1994,
abstract = {A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sn+2. Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y].We will give here a characterization of 2-knot groups in terms of presentations. It has the flavor of Artin's characterization of 1-knot groups. S. Kamada has independently obtained another characterization of 2-knot groups ([Ka]).},
author = {González-Acuña, Francisco},
journal = {Revista Matemática Iberoamericana},
keywords = {Topología algebraica; Grupos de n-anidaciones; Variedad recubridora; Grupo de trenzas; 2-knot groups; closed braids; presentation},
language = {eng},
number = {2},
pages = {221-228},
title = {A characterization of 2-knots groups.},
url = {http://eudml.org/doc/39454},
volume = {10},
year = {1994},
}

TY - JOUR
AU - González-Acuña, Francisco
TI - A characterization of 2-knots groups.
JO - Revista Matemática Iberoamericana
PY - 1994
VL - 10
IS - 2
SP - 221
EP - 228
AB - A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sn+2. Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y].We will give here a characterization of 2-knot groups in terms of presentations. It has the flavor of Artin's characterization of 1-knot groups. S. Kamada has independently obtained another characterization of 2-knot groups ([Ka]).
LA - eng
KW - Topología algebraica; Grupos de n-anidaciones; Variedad recubridora; Grupo de trenzas; 2-knot groups; closed braids; presentation
UR - http://eudml.org/doc/39454
ER -

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