Detected Seifert surfaces and intervals of left-orderable surgeries

2025/09/09 by Yi Wang, Wang, Yi · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.08127

openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Limiting characters at ideal points detecting twice-punctured tori
• The JSJ-decomposition of the 3-manifold obtained by 0-surgery along a classical pretzel knot of genus one
• Punctured JSJ tori and tautological extensions of Azumaya algebras
• A unified Casson-Lin invariant for the real forms of SL(2)
• Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots
• Non-left-orderability of cyclic branched covers of pretzel knots P(3,-3,-2k-1)
• Classical pretzel knots and left orderability
• Left-orderability, branched covers and double twist knots
• Slope of Orderable Dehn Filling of Two-Bridge Knots
• Left orderable surgeries of double twist knots
• Orderability of Homology Spheres Obtained by Dehn Filling
• Left-orderablity for surgeries on (-2,3,2s+1)-pretzel knots
• On left-orderability and cyclic branched coverings
• Character varieties of once-punctured torus bundles with tunnel number one
• On L-spaces and left-orderable fundamental groups
• On L-spaces and left-orderable fundamental groups
• Conway spheres as ideal points of the character variety
• On knot Floer homology and cabling II
• Not all boundary slopes are strongly detected by the character variety
• Orderable 3-manifold groups
• Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds

Cited by

• SL₂(\mathbb R)-representations and left-orderable surgeries of (-2, 3, 2n+1)-pretzel knots

Related

• Order-detection and non-left-orderable surgeries on links
• Non-left-orderable surgeries on twisted torus knots
• JSJ decompositions of knot exteriors, Dehn surgery and the L-space conjecture
• Infinite families of non-left-orderable L-spaces
• Left orderability for surgeries on the [1,1,2,2,2j] two-bridge knots