Alpha Shape Topology of the Cosmic Web

Rien van de Weygaert, Erwin Platen, Gert Vegter, Bob Eldering, Nico Kruithof

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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Abstract

We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers (βk, k = 1, . . . , D), which represent a complete characterization of the topology of a manifold. This forms a useful extension of the geometry and topology of the galaxy distribution by Minkowski functionals, of which three specify the geometrical structure of surfaces and one, the Euler characteristic, represents merely a summary of its topology. In order to develop an intuitive understanding for the relation between Betti numbers and the running α parameter of the alpha shapes, and thus in how far they may discriminate between different topologies, we study them within the context of simple heuristic Voronoi clustering models. These may be tuned to consist of a few or even only one specific morphological element of the Cosmic Web, ie. clusters, filaments or sheets.
Original languageEnglish
Title of host publicationSeventh International Symposium on Voronoi Diagrams in Science and Engineering
Subtitle of host publicationISVD 2010 : proceedings : 28-30 June 2010, Quebec, Canada
PublisherIEEE Computer Society
Number of pages11
ISBN (Print)9781424476060
DOIs
Publication statusPublished - 2010

Keywords

  • Computational Topology
  • Computational Geometry: tessellations
  • Techniques: image processing
  • Methods: data analysis
  • Cosmology: theory - large-scale structure of Universe

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