Hecguard Splittings and genetic structures of 3-manifolds

本项目的主要结果如下：1. Akiyoshi，Sakuma，Wada和Yamashita完成了一份预印本（256页），全面阐述了Jorgensen关于拟Fuchsian穿孔环面群的福特域的理论，并给出了完整的证明。我们计划写一个续集的文件，以解释我们的扩展，他的理论以外的拟fuchsian穿孔环面空间，并解释之间的关系的桥梁结构的2桥结和完整的双曲结构的补充。2.Epstein-Penner通过一个凸船体建设的Minkowski空间中引入了有限体积尖双曲流形的欧氏分解。Akiyoshi-Sakuma将这种构造推广到（可能）无限体积尖点双曲流形，并引入了这些流形的EPH-分解。Akiyoshi-Miyachi-Sakuma将双曲穿孔环面丛的McShane恒等式的Bowditch变分推广到一般双曲穿孔曲面丛。

The main results obtained by this project are as follows.1.Akiyoshi, Sakuma, Wada and Yamashita have completed a preprint (256 pages) which gives a full exposition of Jorgensen's theory for the Ford domains of quasifuchsian punctured torus groups, including a full proof. We plan to write a sequel of the paper to explain our extension of his theory to the outside of the quasifuchsian punctured torus space and to explain the relationship between the bridge structure of a 2-bridge knot and the complete hyperbolic structure of its complement.2.Epstein-Penner has introduced the Euclidean decompositions of finite-volume cusped hyperbolic manifolds through a convex hull construction in the Minkowski space. Akiyoshi-Sakuma has generalized the construction to (possibly) infinite-volume cusped hyperbolic manifolds and introduced EPH-decompositions of these manifolds. Moreover, relation between the EPH-decompositions and the bending laminations of cusped hyper-bolic manifolds were studied by Akiyoshi-Sakuma-Wada Yamashita.3.Akiyoshi-Miyachi-Sakuma have generalized Bowditch's variation of McShane's identity for hyperbolic punctured torus bundles to general hyperbolic punctured surface bundles.