School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia.
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia
Proc Natl Acad Sci U S A. 2018 Oct 23;115(43):10908-10913. doi: 10.1073/pnas.1718961115.
This paper describes a generalization of Heegaard splittings of 3-manifolds and trisections of 4-manifolds to all dimensions, using triangulations as a key tool. In particular, every closed piecewise linear n-manifold can be divided into [Formula: see text] n-dimensional 1-handlebodies, where [Formula: see text] or [Formula: see text], such that intersections of the handlebodies have spines of small dimensions. Several applications, constructions, and generalizations of our approach are given.
本文使用三角剖分作为关键工具，将 3-流形的 Heegaard 剖分和 4-流形的 trisec-tion 推广到所有维度。具体来说，每个封闭分段线性 n-流形都可以被分割成[公式：见正文]个 n 维 1-柄体，其中[公式：见正文]或[公式：见正文]，使得柄体的交集具有小维数的脊柱。给出了我们方法的几个应用、构造和推广。
