Quantifying the topology of large-scale structure | Zendy

Peter Coles | Zendy; Andrew G. Davies | Zendy; R. C. Pearson | Zendy

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Quantifying the topology of large-scale structure

Author(s) -

Peter Coles,

Andrew G. Davies,

R. C. Pearson

Publication year - 1996

Publication title -

monthly notices of the royal astronomical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.058

H-Index - 383

eISSN - 1365-8711

pISSN - 0035-8711

DOI - 10.1093/mnras/281.4.1375

Subject(s) - physics , topology (electrical circuits) , scale (ratio) , differential (mechanical device) , differential geometry , algorithm , theoretical physics , geometry , computer science , mathematics , quantum mechanics , combinatorics , thermodynamics

We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological characteristics, based on concepts, on the one hand, from differential topology and, on the other, from integral geometry. The former approach leads one to concentrate on properties of the contour surfaces which, in turn, leads to the algorithms CONTOUR2D and CONTOUR3D familiar to cosmologists. The other approach, which we adopt here, actually leads to much simpler algorithms in both two and three dimensions. (The 2D algorithm has already been introduced to the astronomical literature.) We discuss the 3D case in some detail and compare results obtained with it to analogous results using the CONTOUR3D algorithm

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