Left-orderability for surgeries on twisted torus knots

2018/09/04 by Anh T. Tran, Tran, Anh T. · 1 citation
Computer Science · Mathematics · #57M05 #57M25 (Secondary) #57M27 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M05 #msc:57M25 #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1809.01250

6 pages

arxiv created 2018/09/04 · openalex publication_date 2018/09/04 · arxiv updated 2018/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the fundamental group of the 3-manifold obtained by (p)/(q)-surgery along the (n-2)-twisted (3,3m+2)-torus knot, with n,m ≥ 1, is not left-orderable if (p)/(q) ≥ 2n + 6m-3 and is left-orderable if (p)/(q) is sufficiently close to 0.

Citations

• On L-spaces and left-orderable fundamental groups
• A note on orderability and Dehn filling

Cited by

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

Related

• Non left-orderable surgeries on L-space twisted torus knots
• SL₂(\mathbb R)-representations and left-orderable surgeries of (-2, 3, 2n+1)-pretzel knots
• Non left-orderable surgeries on negatively twisted torus knots
• Non-left-orderable surgeries on twisted torus knots
• An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery