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تسجيل مستخدم جديدAlpha Shape Topology of the Cosmic Web
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تأليف
Rien van de Weygaert
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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 ($beta_{rm k},k=1,...,D$), 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 a key aspect of its topology. In order to develop an intuitive understanding for the relation between Betti numbers and the running $alpha$ 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.
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We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend
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