Multisections of piecewise linear manifolds

J. Hyam Rubinstein; Stephan Tillmann

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arXiv · 1602.03279

Multisections of piecewise linear manifolds

J. Hyam Rubinstein·Stephan Tillmann

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Abstract

Recently Gay and Kirby described a new decomposition of smooth closed $4$-manifolds called a trisection. This paper generalises Heegaard splittings of $3$-manifolds and trisections of $4$-manifolds to all dimensions, using triangulations as a key tool. In particular, we prove that every closed piecewise linear $n$-manifold has a multisection, i.e. 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 generalisations of our approach are given.

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BibTeX RIS

J. Hyam Rubinstein, Stephan Tillmann. 2016-02-10. Multisections of piecewise linear manifolds. https://arxiv.org/abs/1602.03279

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