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arXiv · 2509.08127

Detected Seifert surfaces and intervals of left-orderable surgeries

Yi Wang
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Abstract

Motivated by the $L$-space conjecture, we prove left-orderability of certain Dehn fillings on integral homology solid tori with techniques first appearing in the work of Culler-Dunfield. First, we use the author's previous results to construct arcs of representations originating at ideal points detecting Seifert surfaces inside certain 3-manifolds. This, combined with the holonomy extension locus techniques of Gao, proves that Dehn fillings near 0 of such 3-manifolds are left-orderable. We then explicitly verify the hypotheses of the main theorem for an infinite collection of odd pretzel knots, establishing previously unknown intervals of orderable Dehn fillings. This verifies the $L$-space conjecture for a new infinite family of closed 3-manifolds.

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Yi Wang. 2025-09-09. Detected Seifert surfaces and intervals of left-orderable surgeries. https://arxiv.org/abs/2509.08127

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