Journal article

Generalized trisections in all dimensions

J Hyam Rubinstein, Stephan Tillmann

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | NATL ACAD SCIENCES | Published : 2018

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.

Grants

Awarded by DFG Collaborative Center


Awarded by Australian Research Council


Funding Acknowledgements

S.T. thanks the DFG Collaborative Center (SFB/TRR 109) "Discretization in Geometry and Dynamics," where parts of this work have been carried out, for its hospitality. The authors are partially supported under the Australian Research Council's Discovery funding scheme (Project DP160104502).