Volume Conjecture and its generalizations

体积猜想及其推广

• 批准号: 22540069
• 负责人: MURAKAMI Hitoshi
• 金额: $ 2.75万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540069/
• 关键词: 位相幾何; 結び目; 体積予想; Jones多項式; 色付きJones多項式; 体積; Chern-Simons不変量; Reidemeister torsion; colored Jones 多項式; HOMFLY多項式; Chem-Simons不変量; 基本群の表現

The volume conjecture states that by studying a certain asymptotic behavior of the colored Jones polynomial of a knot would tell us the volume of the knot complement. It was proposed by R. Kashaev, J. Murakami and the main investigator. Now the conjecture is generalized to various ways and attracts many researchers including theoretical physicists. In this research we solve part of the conjecture, give yet more generalizations, and solve part of these generalizations.

体积的猜想指出，通过研究彩色琼斯多项式的某种渐近行为，可以告诉我们结的体积。它是由R. Kashaev，J。Murakami和主要研究人员提出的。现在，猜想被推广到各种方式，并吸引了包括理论物理学家在内的许多研究人员。在这项研究中，我们解决了部分猜想，进行了更多的概括，并解决了部分概括。

项目成果

Superconformal algebra, mock theta function, and Mathieu moonshine

超共形代数、模拟 theta 函数和 Mathieu 私酒

• 发表时间: 2011
• 作者: 松本剛昭;本間健二;Kazuhiro Hikami
• 通讯作者: Kazuhiro Hikami

Cluster algebra and complex volume of 2-bridge knots

簇代数和 2 桥结的复体积

• 作者: Jishan Fan;H. Gao;T. Ogawa;and F. Takahashi;K. Hikami
• 通讯作者: K. Hikami

N=4 superconfor mal algebra and the entropy of hyperKahler manifolds.

N=4 超共形马尔代数和超卡勒流形的熵。

• 发表时间: 2010
• 期刊: J. High Energy Phys.
• 作者: Eguchi;Tohru and Hikami;Kazuhiro;印南信宏;藤岡敦;印南信宏;藤岡敦;H.Murakami;印南信宏;藤岡敦;印南信宏;藤岡敦;Tohru Eguchi and Kazuhiro Hikami;藤岡敦;Tohru Eguchi and Kazuhiro Hikami
• 通讯作者: Tohru Eguchi and Kazuhiro Hikami

An introduction to the volume conjecture. Interactions between hyperbolic geometry, quantum topology and number theory

体积猜想简介。

• 发表时间: 2011
• 期刊: Contemp. Math., Amer. Math. Soc., Providence, RI
• 作者: Kathrin Bringmann;Kazuhiro Hikami;and Jeremy Lovejoy;Nobuhiro Innami;藤岡敦;Igor Belegradek;藤岡敦;Hitoshi Murakami
• 通讯作者: Hitoshi Murakami

N=2Superconformal algebras and the entropy of Calabi-Yau manifolds

N=2超共形代数和Calabi-Yau流形的熵

• 发表时间: 2010
• 期刊: Lett. Math. Phys.92
• 作者: Eguchi;Tohru and Hikami;Kazuhiro;印南信宏;藤岡敦;印南信宏;藤岡敦;H.Murakami;印南信宏;藤岡敦;印南信宏;藤岡敦;Tohru Eguchi and Kazuhiro Hikami
• 通讯作者: Tohru Eguchi and Kazuhiro Hikami