A combinatorial approach to obstructing left-orderability of Dehn fillings

2026/07/17 by Adam Clay, Junyu Lu, Tjay Staruch
#math.GT

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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 S³ 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.

Citations

• On L-spaces and left-orderable fundamental groups

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