HNN EXTENSION OF CYCLICALLY PRESENTED GROUPS-Reference-Cited by-同舟云学术

HNN EXTENSION OF CYCLICALLY PRESENTED GROUPS

Published:2001-12 Issue:08 Volume:10 Page:1269-1279
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

SZCZEPAŃSKI ANDRZEJ¹,VESNIN ANDREI²

Affiliation:

1. Institute of Mathematics, University of Gdańsk, ul. Wita Stwoza 57, 80-952, Gdańsk, Poland

2. Sobolev Institute of Mathematics, pr. Koptyuga 4, Novosibirsk 630090, Russia

Abstract

It is shown that if the defining word of a cyclically presented group is admissable then its natural HNN extension is the group of a high dimensional knot. As an example we define a family of cyclically presented groups which contains Sieradski groups, Fibonacci groups, and Gilbert-Howie groups. It is proven that HNN extensions of these groups are LOG groups and so, are fundamental groups of complements of codimension two closed orientable connected tamely embeded ℓ-dimensional manifolds (ℓ≥2).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216501001438

Reference10 articles.

1. On manifold spines and cyclic presentations of groups

2. LOG Groups and Cyclically Presented Groups

3. Abelian normal subgroups of two-knot groups

4. On the asphericity of ribbon disc complements

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