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Development of software to and researches in hyperbolic geometry and kleinnian group

双曲几何与克莱尼群的软件开发与研究

基本信息

批准号：
11640078
负责人：
WADA Masaki
金额：
$ 1.41万
依托单位：
Nara Women's University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640078/
关键词：
hyperbolic geometry kleinnian group research-aid software

项目摘要

In this project, we have developed a research tool OPTi for researchers in hyperbolic geometry and Kleinnian groups, and improved it in various ways. The results obtained in the project have always been open to the public through the OPTi Home Page (RUL: http://vivaldi.ics.nara-wu.ac.jp/〜wada/OPTi/index.html). We gave talks related to OPTi in many conferences and workshops including The 5th International Conference in Clifford Algebra, Mexico, 1999, Workshop on Computations in Group Theory and Geometry, University of Warwick, 1999, Workshop on Kleinian Groups and Hyperbolic 3-Manifolds, University of Warwick, 2001. We also organized workshops "Punctured tori and 2-bridge knots ", Nara Women's University, 2000 and "Studies on Geometric 3-orbifolds", Nara Women's Univeristy, 2000, and heard comments and 1 requests about OPTi from many researchers. As a result, OPTi has become much more useful and is much easier to use than the first version.Meanwhile, in 2001, in cooperation with Yamashita, Sugawa and Komori, we applied the algorithm for drawing the Ford regions used in OPTi to the Bers slice, and obtained pictures of the exotic components for the first time in the world. The algorithm used therein was later implemented into OPTi Version 3.30 to give real-time drawing of the deformations of various kinds of slice pictures.

在这个项目中，我们为双曲几何和Kleinnian群的研究人员开发了一个研究工具OPTi，并对其进行了各种改进。项目中获得的成果一直通过OPTi主页（RUL: http://vivaldi.ics.nara-wu.ac.jp/ ~ wada/OPTi/index.html）向公众开放。我们在许多会议和研讨会上发表了与OPTi相关的演讲，包括1999年第五届克利福德代数国际会议，墨西哥，华威大学，1999年群论和几何计算研讨会，2001年华威大学，Kleinian群和双曲3-流形研讨会。我们还组织了研讨会“穿孔环纹和2桥结”，奈良女子大学，2000年和“几何3-轨道的研究”，奈良女子大学，2000年，听取了许多研究人员对OPTi的评论和要求。因此，OPTi比第一个版本变得更有用，更容易使用。同时，在2001年，我们与Yamashita， Sugawa和Komori合作，将OPTi中使用的Ford区域绘制算法应用到Bers切片上，并在世界上首次获得了奇异部件的图像。其中使用的算法后来在OPTi 3.30版本中实现，可以实时绘制各种切片图的变形。