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DOI: 10.4230/LIPIcs.SoCG.2018.71

The Trisection Genus of Standard Simply Connected PL 4-Manifolds

Authors: Jonathan Spreer and Stephan Tillmann

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract

Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. In this note we show that the K3 surface has trisection genus 22. This implies that the trisection genus of all standard simply connected PL 4-manifolds is known. We show that the trisection genus of each of these manifolds is realised by a trisection that is supported by a singular triangulation. Moreover, we explicitly give the building blocks to construct these triangulations.

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Jonathan Spreer and Stephan Tillmann. The Trisection Genus of Standard Simply Connected PL 4-Manifolds. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 71:1-71:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{spreer_et_al:LIPIcs.SoCG.2018.71,
  author =	{Spreer, Jonathan and Tillmann, Stephan},
  title =	{{The Trisection Genus of Standard Simply Connected PL 4-Manifolds}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{71:1--71:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.71},
  URN =		{urn:nbn:de:0030-drops-87847},
  doi =		{10.4230/LIPIcs.SoCG.2018.71},
  annote =	{Keywords: combinatorial topology, triangulated manifolds, simply connected 4-manifolds, K3 surface, trisections of 4-manifolds}
}

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The Trisection Genus of Standard Simply Connected PL 4-Manifolds

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