On knot groups acting on trees

2018/07/17 by F. A. Dudkin, Dudkin, Fedor, A. S. Mamontov +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #20E06 #20E08 #20F65 #Cellular transport and secretion #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1807.06275

openalex publication_date 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 1-knot group G is GBS group iff G is a torus-knot group and describe all n-knot GBS groups for n\geqslant 3.

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