THE COMPLEX VOLUMES OF TWIST KNOTS

被引：13

作者：

Cho, Jinseok ^{[1
]}

Murakami, Jun ^{[2
]}

Yokota, Yoshiyuki ^{[3
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151742, South Korea

[2] Waseda Univ, Fac Sci & Engn, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan

[3] Tokyo Metropolitan Univ, Dept Math, Tokyo 1920397, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 10期

关键词：

Twist knot; volume conjecture; complex volume;

D O I：

10.1090/S0002-9939-09-09906-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a given hyperbolic knot, the third author defined a function whose imaginary part gives the hyperbolic volume of the knot complement. We show that, for a twist knot, the function actually gives the complex volume of the knot complement using Zickert's and Neumann's theory of the extended Bloch groups and the complex volumes.

引用

页码：3533 / 3541

页数：9

共 42 条

[31] Proof of the Volume Conjecture for Whitehead Doubles of a Family of Torus Knots [J].

Hao ZHENG Department of MathematicsZhongshan UniversityGuangzhou China .

ChineseAnnalsofMathematics, 2007, (04) :375-388

[32] On the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings [J].

Ohtsuki, Tomotada .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2017, 28 (13)

[33] Twisted Alexander polynomials with the adjoint action for some classes of knots [J].

Tran, Anh T. .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2014, 23 (10)

[34] TWISTED ALEXANDER POLYNOMIALS OF GENUS ONE TWO-BRIDGE KNOTS [J].

Tran, Anh T. .

KODAI MATHEMATICAL JOURNAL, 2018, 41 (01) :86-97

[35] An L2-Alexander-Conway invariant for knots and the volume conjecture [J].

Li, Weiping ;

Zhang, Weiping .

DIFFERENTIAL GEOMETRY AND PHYSICS, 2006, 10 :303-+

[36] Symplectic quandles and parabolic representations of 2-bridge knots and links [J].

Jo, Kyeonghee ;

Kim, Hyuk .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2020, 31 (10)

[37] Kashaev's conjecture and the Chern-Simons invariants of knots and links [J].

Murakami, H ;

Murakami, J ;

Okamoto, M ;

Takata, T ;

Yokota, Y .

EXPERIMENTAL MATHEMATICS, 2002, 11 (03) :427-435

[38] Quantum invariants of three-manifolds obtained by surgeries along torus knots [J].

Murakami, Hitoshi ;

Tran, Anh T. .

QUANTUM TOPOLOGY, 2022, 13 (04) :691-795

[39] Slavik Jablan's last notes on the Chern-Simons invariants of knots [J].

Stosic, Marko .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2016, 25 (09)

[40] The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries [J].

Murakami, H .

FUNDAMENTA MATHEMATICAE, 2004, 184 :269-289

← 1 2 3 4 5 →