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On the combinatorics of veering triangulations

关于转向三角测量的组合学

基本信息

批准号：
1936817
负责人：
金额：
--
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-1936817
关键词：
combinatorics veering triangulations

项目摘要

In the 1970's and 1980's William Thurston revolutionised low-dimensional topology. He introduced many new ideas into the field, and furthermore revealed exciting connections between the combinatorial study of three-manifolds and many other areas:Teichmuller theory, holomorphic dynamics, Kleinian groups, geometric group theory, and more.One of the new techniques he pioneered was the use of ideal triangulations to represent hyperbolic three-manifolds. This allowed topologists, on the one hand, access to tools in algebraic geometry and, on the other hand, an organising principle for what had been a hodge-podge of disparate examples. The idea of ideal triangulations has now been generalised and specialised many times to give angled triangulations [Casson], taut ideal triangulations [Lackenby], and veering triangulations [Agol, HRST].Francois Gueritaud has found an important connection between the Cannon-Thurston map for fibered manifolds and their veering triangulations. Yair Minsky and Samuel Taylor have given an interesting relation between the machinary of subsurface projections and the structure of veering triangulations. The goal of this project is to understand how the combinatorics of a veering triangulation, in the non-fibered setting, inform the cooresponding Cannon-Thurston map and the "fibered structure" of the universal cover of the three-manifold.

在20世纪70年代和80年代的威廉瑟斯顿革命性的低维拓扑结构。他介绍了许多新的想法进入该领域，并进一步揭示了令人兴奋的连接之间的组合研究的三流形和许多其他领域：Teichmuller理论，全纯动力学，Kleinian群，几何群论，和更多的新技术之一，他开创了使用理想的三角形，以代表双曲三流形。这使得拓扑学家，一方面，获得工具的代数几何，另一方面，一个组织原则，什么一直是大杂烩的不同的例子。理想的三角形的想法现在已经普遍化和专门化多次给角三角形[卡森]，紧张的理想三角形[Lackenby]，和转向三角形[阿戈尔，HRST]。弗朗索瓦Gueritaud发现了一个重要的连接之间的大炮，瑟斯顿地图纤维流形和他们的转向三角形。Yair Minsky和Samuel Taylor给出了地下投影的机器和转向三角剖分的结构之间的有趣关系。这个项目的目标是了解如何转向三角形的组合学，在非纤维设置，通知cooorresponding Cannon-Thurston映射和“纤维结构”的三个流形的通用覆盖。