2014/03/08 by Ji-Young Ham, Alexander Mednykh, Ham, Ji-young +3 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1403.1941
openalex publication_date 2014/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in terms of the distance between the two axes fixed by two generators. In this way the calculation becomes easier than using the singular locus directly. The volumes of the hyperbolic twist knot cone-manifolds simpler than Stevedore's knot are known. As an application, we give the volumes of the cyclic coverings over the hyperbolic twist knots.