Journal article
Computing trisections of 4-manifolds
Mark Bell, Joel Hass, Joachim Hyam Rubinstein, Stephan Tillmann
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | NATL ACAD SCIENCES | Published : 2018
Abstract
We describe an algorithm to compute trisections of orientable four-manifolds using arbitrary triangulations as input. This results in explicit complexity bounds for the trisection genus of a 4-manifold in terms of the number of pentachora (4-simplices) in a triangulation.
Grants
Awarded by National Science Foundation
Awarded by Australian Research Council
Awarded by Deutsche Forschungsgemeinschaft Collaborative Center at Technische Universitat Berlin
Funding Acknowledgements
We thank the American Institute for Mathematics and the organizers of the workshop Trisections and Low-Dimensional Topology, where this work was initiated, and thank Jeff Meier and Jonathan Spreer for helpful discussions. We also thank the anonymous referee for helpful comments. J.H. was partially supported by National Science Foundation Grant DMS-1719582-0. The research of J.H. R.and S.T. is partially supported by Australian Research Council Discovery Funding Scheme Project DP160104502. S.T. thanks the Deutsche Forschungsgemeinschaft Collaborative Center Transregionaler Sonderforschungsbereich 109 at Technische Universitat Berlin, where parts of this work have been carried out, for its hospitality.