| 书目名称 | Volume Conjecture for Knots |
| 编辑 | Hitoshi Murakami,Yoshiyuki Yokota |
| 视频video | |
| 概述 | Provides a short but effective introduction to quantum invariants of knots and links.Provides a short but effective introduction to the geometry of a knot complement.Gives the current status of the vo |
| 丛书名称 | SpringerBriefs in Mathematical Physics |
| 图书封面 |  |
| 描述 | .The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called .R.-matrix that is associated with the .N.-dimensional representation of the Lie algebra sl(2;.C.). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the .N.-dimensional colored Jones polynomial evaluated at the .N.th. root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume..In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the |
| 出版日期 | Book 2018 |
| 关键词 | Volume conjecture; Colored Jones polynomial; Knot; Chern-Simons invariant; Hyperbolic geometry |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-13-1150-5 |
| isbn_softcover | 978-981-13-1149-9 |
| isbn_ebook | 978-981-13-1150-5Series ISSN 2197-1757 Series E-ISSN 2197-1765 |
| issn_series | 2197-1757 |
| copyright | The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018 |
发表于 2025-3-21 16:03:49
