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Documents authored by Burke, Rhuaidi Antonio

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Software
DOI: 10.4230/artifacts.23281
raburke/Dim4Census

Authors: Rhuaidi Antonio Burke, Benjamin A. Burton, and Jonathan Spreer

Abstract
Cite as

Rhuaidi Antonio Burke, Benjamin A. Burton, Jonathan Spreer. raburke/Dim4Census (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23281,
   title = {{raburke/Dim4Census}}, 
   author = {Burke, Rhuaidi Antonio and Burton, Benjamin A. and Spreer, Jonathan},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:ee5ac0c76fdef9983c5de8a0be93f7684dd9a796;origin=https://github.com/raburke/Dim4Census;visit=swh:1:snp:a7fee9b4ed22b6bf281127e889c432095a216a58;anchor=swh:1:rev:54753c465209c14b34834a5f13cfe373b53ca4c6}{\texttt{swh:1:dir:ee5ac0c76fdef9983c5de8a0be93f7684dd9a796}} (visited on 2025-06-20)},
   url = {https://github.com/raburke/Dim4Census},
   doi = {10.4230/artifacts.23281},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.28
Small Triangulations of 4-Manifolds and the 4-Manifold Census

Authors: Rhuaidi Antonio Burke, Benjamin A. Burton, and Jonathan Spreer

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We present a framework to classify PL-types of large censuses of triangulated 4-manifolds, which we use to classify the PL-types of all triangulated 4-manifolds with up to 6 pentachora. This is successful except for triangulations homeomorphic to the 4-sphere, CP², and the rational homology sphere QS⁴(2), where we find at most four, three, and two PL-types respectively. We conjecture that they are all standard. In addition, we look at the cases resisting classification and discuss the combinatorial structure of these triangulations - which we deem interesting in their own rights.
Cite as

Rhuaidi Antonio Burke, Benjamin A. Burton, and Jonathan Spreer. Small Triangulations of 4-Manifolds and the 4-Manifold Census. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{burke_et_al:LIPIcs.SoCG.2025.28,
  author =	{Burke, Rhuaidi Antonio and Burton, Benjamin A. and Spreer, Jonathan},
  title =	{{Small Triangulations of 4-Manifolds and the 4-Manifold Census}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.28},
  URN =		{urn:nbn:de:0030-drops-231805},
  doi =		{10.4230/LIPIcs.SoCG.2025.28},
  annote =	{Keywords: computational low-dimensional topology, triangulations, census of triangulations, 4-manifolds, PL standard 4-sphere, Pachner graph, mathematical software, experiments in low-dimensional topology}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.29
Practical Software for Triangulating and Simplifying 4-Manifolds

Authors: Rhuaidi Antonio Burke

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
Dimension 4 is the first dimension in which exotic smooth manifold pairs appear - manifolds which are topologically the same but for which there is no smooth deformation of one into the other. Whilst smooth and triangulated 4-manifolds do coincide, comparatively little work has been done towards gaining an understanding of smooth 4-manifolds from the discrete and algorithmic perspective. In this paper we introduce new software tools to make this possible, including a software implementation of an algorithm which enables us to build triangulations of 4-manifolds from Kirby diagrams, as well as a new heuristic for simplifying 4-manifold triangulations. Using these tools, we present new triangulations of several bounded exotic pairs, corks and plugs (objects responsible for "exoticity"), as well as the smallest known triangulation of the fundamental K3 surface. The small size of these triangulations benefit us by revealing fine structural features in 4-manifold triangulations.
Cite as

Rhuaidi Antonio Burke. Practical Software for Triangulating and Simplifying 4-Manifolds. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{burke:LIPIcs.SoCG.2024.29,
  author =	{Burke, Rhuaidi Antonio},
  title =	{{Practical Software for Triangulating and Simplifying 4-Manifolds}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.29},
  URN =		{urn:nbn:de:0030-drops-199748},
  doi =		{10.4230/LIPIcs.SoCG.2024.29},
  annote =	{Keywords: computational low-dimensional topology, triangulations, 4-manifolds, exotic 4-manifolds, mathematical software, experiments in low-dimensional topology}
}
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