Orderability of homology spheres obtained by Dehn filling

DOI10.4310/MRL.2022.V29.N5.A4zbMATH Open1530.57015arXiv1810.11202OpenAlexW4366674911MaRDI QIDQ6042853

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Publication date: 4 May 2023

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Abstract: In this paper, we develop a method for constructing left-orders on the fundamental groups of rational homology 3-spheres. We begin by constructing the holonomy extension locus of a rational homology solid torus $M$, which encodes the information about peripherally hyperbolic $widetildeext{PSL}_{2}mathbbR$ representations of $p{i}_1(M)$. Plots of the holonomy extension loci of many rational homology solid tori are shown, and the relation to left-orderability is hinted. Using holonomy extension loci, we study rational homology 3-spheres coming from Dehn filling on rational homology solid tori and construct intervals of Dehn fillings with left-orderable fundamental group.

Full work available at URL: https://arxiv.org/abs/1810.11202

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