Generalized trisections in all dimensions.
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- Record sourced from PubMed, PMID 30348761.
- Also identified by DOI 10.1073/pnas.1718961115 and PMC identifier 6205469.
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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 [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.