Detected Seifert surfaces and intervals of left-orderable surgeries
Abstract
Motivated by the -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 -space conjecture for a new infinite family of closed 3-manifolds.
Cite
@article{arxiv.2509.08127,
title = {Detected Seifert surfaces and intervals of left-orderable surgeries},
author = {Yi Wang},
journal= {arXiv preprint arXiv:2509.08127},
year = {2025}
}