Orderability of Homology Spheres Obtained by Dehn Filling

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.

32 pages, 20 figures. arXiv admin note: text overlap with arXiv:1602.03793 by other authors

References in corpus (1)

• Mahler's Measure and the Dilogarithm (II)

Cited by in corpus (3)

• Euler class of taut foliations and Dehn filling
• Left orderable surgeries of double twist knots II
• Left orderability for surgeries on the $[1,1,2,2,2j]$ two-bridge knots