Author:
Rubinstein J. Hyam,Tillmann Stephan
Abstract
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=2k+1 or n=2k, such that intersections of the handlebodies have spines of small dimensions. Several applications, constructions, and generalizations of our approach are given.
Funder
Australian Research Council
Publisher
Proceedings of the National Academy of Sciences
Reference24 articles.
1. Trisecting 4-manifolds;Gay;Geom Topol,2016
2. Introduction of a Riemannian geometry on a triangulable 4-manifold;Cairns;Ann Math,1944
3. The manifold smoothing problem;Cairns;Bull Am Math Soc,1961
4. On
C
1
-complexes;Whitehead;Ann Math,1940
5. Rubinstein JH Tillmann S (2016) Multisections of piecewise linear manifolds. arXiv:1602.03279v1.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献