Orderability of Homology Spheres Obtained by Dehn Filling

Xinghua Gao

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arXiv · 1810.11202

Orderability of Homology Spheres Obtained by Dehn Filling

Xinghua Gao

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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 $\widetilde{\text{PSL}_2\mathbb{R}}$ representations of $\pi_1(M)$. 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.

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Xinghua Gao. 2018-10-26. Orderability of Homology Spheres Obtained by Dehn Filling. https://arxiv.org/abs/1810.11202

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