期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2018
卷号：115
期号：43
页码：10908-10913
DOI：10.1073/pnas.1718961115
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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 k + 1 n-dimensional 1-handlebodies, where n = 2 k + 1 or n = 2 k , such that intersections of the handlebodies have spines of small dimensions. Several applications, constructions, and generalizations of our approach are given.
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