One-relator Sasakian groups
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 159-170
MSC: Primary 57M50, 32Q15, 57M05; Secondary 14F35, 32J15.
DOI: 10.4064/cm8521-3-2021
Published online: 28 May 2021
Abstract
We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus $g \gt 0$ with at most one orbifold point of order $n \geq 1$. We also classify all groups of deficiency at least 2 that are also the fundamental group of some compact Sasakian manifold.
