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Multisections of Piecewise Linear Manifolds by Rubinstein, J. Hyam; Tillmann, Stephan is a scholarly article available to read on EtoBox.

What is Multisections of Piecewise Linear Manifolds about?

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.

Author

Rubinstein, J. Hyam; Tillmann, Stephan

Published

2016

Language

EN