
TL;DR
This paper characterizes which one-relator groups can be fundamental groups of compact Sasakian manifolds, showing they are either finite cyclic or related to Riemann surface groups, and classifies high-deficiency groups with this property.
Contribution
It provides a complete classification of one-relator and high-deficiency groups that are fundamental groups of compact Sasakian manifolds.
Findings
One-relator groups are Sasakian iff they are finite cyclic or surface groups with orbifold points.
Classifies all high-deficiency groups that are Sasakian.
Establishes a clear criterion linking group properties to Sasakian geometry.
Abstract
We prove that any one-relator group is the fundamental group of a compact Sasakian manifold if and only if is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order . We also classify all groups of deficiency at least two that are also the fundamental group of some compact Sasakian manifold.
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