The volume of hyperbolic cone-manifolds of the knot with Conway's notation C(2n, 3)
- Authors
- Ham, Ji-Young; Lee, Joongul
- Issue Date
- May-2016
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Hyperbolic orbifold; hyperbolic cone-manifold; volume; C(2n, 3); orbifold covering; Riley-Mednykh polynomial
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.25, no.6
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 25
- Number
- 6
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/13405
- DOI
- 10.1142/S0218216516500309
- ISSN
- 0218-2165
- Abstract
- Let C(2n, 3) be the family of two bridge knots of slope (4n+1)/(6n+1). We calculate the volumes of the C(2n, 3) cone-manifolds using the Schlafli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano and Montesinos-Amilibia and extend the Ham, Mednykh and Petrov's methods. As an application, we give the volumes of the cyclic coverings over those knots. For the fundamental group of C(2n, 3), we take and tailor Hoste and Shanahan's. As a byproduct, we give an affirmative answer for their question whether their presentation is actually derived from Schubert's canonical two-bridge diagram or not.
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Collections - College of Education > Department of Mathematics Education > 1. Journal Articles
- College of Engineering > Department of Science > 1. Journal Articles
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