A combinatorial approach to obstructing left-orderability of Dehn fillings

Adam Clay; Junyu Lu; Tjay Staruch

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arXiv · 2607.15603

A combinatorial approach to obstructing left-orderability of Dehn fillings

Adam Clay·Junyu Lu·Tjay Staruch

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Abstract

We introduce the conjugate-slope property of knots, a variant of Nie's Property (D), which can be used to study non-left-orderability of fundamental groups arising from Dehn filling. We show that this property holds for any knot in $S^3$ admitting a diagram whose negative crossings can be "controlled" in a precise combinatorial sense. The conjugate-slope property also places strong restrictions on the kinds of left-orderings that the knot group can support, and implies that the image of the meridian is generalised torsion in the fundamental group of many of the knot's Dehn fillings.

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BibTeX RIS

Adam Clay, Junyu Lu, Tjay Staruch. 2026-07-17. A combinatorial approach to obstructing left-orderability of Dehn fillings. https://arxiv.org/abs/2607.15603

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