One-relator Sasakian groups

Indranil Biswas, Mahan Mj Colloquium Mathematicum 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.

Authors

  • Indranil BiswasSchool of Mathematics
    Tata Institute of Fundamental Research
    1 Homi Bhabha Road
    Mumbai 400005, India
    e-mail
  • Mahan MjSchool of Mathematics
    Tata Institute of Fundamental Research
    1 Homi Bhabha Road
    Mumbai 400005, India
    e-mail

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