高维广义三分。
Generalized trisections in all dimensions.
机构信息
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
出版信息
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。
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