On left-orderable fundamental groups and Dehn surgeries on twist knots

2013/01/04 by Anh T. Tran, Tran, Anh T.
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M27 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1301.0665

openalex publication_date 2013/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the resulting manifold by r-surgery on the hyperbolic twist knot K_m, m ≥ 2, has left-orderable fundamental group if the slope r satisfies the condition r ∈ (-4,2m) if m is even, and r ∈ [0,4] ∪ (\frac4mω+4, 2m+4) if m is odd, where ω>1 is the unique real solution of the equation x e^x=4m.

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