Explicit formulae for Chern–Simons invariants of the hyperbolic orbifolds of the knot with Conway’s notation C(2n, 3)

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• 作者：Ji-Young Ham ; Joongul Lee
• 关键词：Chern–Simons invariant ; \(C(2n ; 3)\) ; Orbifold ; Riley–Mednykh polynomial ; Orbifold covering
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：107
• 期：3
• 页码：427-437
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

We calculate the Chern–Simons invariants of the hyperbolic orbifolds of the knot with Conway’s notation C(2n, 3) using the Schläfli formula for the generalized Chern–Simons function on the family of C(2n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee’s methods. As an application, we calculate the Chern–Simons invariants of cyclic coverings of the hyperbolic C(2n, 3) orbifolds.