Research ArticleNo Access

On knot groups acting on trees

Fedor A. Dudkin

Sobolev Institute of Mathematics, Novosibirsk State University, 630090 Novosibirsk, Russia

E-mail Address: dudkinF@math.nsc.ru

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and

Andrey S. Mamontov

http://orcid.org/0000-0002-0324-5287

Sobolev Institute of Mathematics, Novosibirsk State University, 630090 Novosibirsk, Russia

E-mail Address: mamontov@math.nsc.ru

Corresponding author.

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https://doi.org/10.1142/S0218216520500625Cited by:2 (Source: Crossref)

Abstract

A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag–Solitar group (GBS group). We prove that a one-knot group $G$ is a GBS group if and only if $G$ is a torus knot group, and describe all n-knot GBS groups for $n \geq 3$ .

Keywords:

AMSC: 20E06, 57M25, 57Q45

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