Communications in Analysis and Geometry

Volume 26 (2018)

Number 3

$3$-manifolds and generalized Baumslag–Solitar groups

Pages: 571 – 584

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n3.a4

Authors

Alberto L. Delgado (Department of Mathematics, Illinois State University, Normal, Il., U.S.A.)

Derek J. S. Robinson (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)

Mathew Timm (Department of Mathematics, Bradley University, Peoria, Illinois, U.S.A.)

Abstract

This article studies the relationship between $3$-manifolds and generalized Baumslag–Solitar groups. We classify the generalized Baumslag–Solitar groups that are fundamental groups of compact orientable $3$-manifolds. More generally, we show that many generalized Baumslag–Solitar groups which are not $3$-manifold groups are special types of quotients of generalized Baumslag–Solitar groups.

Keywords

generalized Baumslag–Solitar group, $3$-manifold group

2010 Mathematics Subject Classification

Primary 20E06, 57M07. Secondary 57M15, 57M20.

Received 15 May 2013

Published 27 July 2018