Strongly Proximal Edelsbrunner-Harer Nerves in Voronoi Tessellations

2016/04/15 by J. F. Peters, Peters, J. F., E. Inan +1
Mathematics · #52A01 #54E05 #57Q10 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52A01 #msc:54E05 #msc:57Q10

paper · pdf · doi:10.48550/arxiv.1604.05249

10 pages, 4 figures

arxiv created 2016/04/15 · arxiv updated 2016/04/19

Abstract

This paper introduces Edelsbrunner-Harer nerve in collections of Voronoi regions (called nucleus clusters) endowed with one or more proximity relations. The main results in this paper are that a maximal nucleus cluster (MNC) in a Voronoi Tessellation is a strongly proximal Edelsbrunner-Harer nerve, each MNC nerve and the union of the sets in the MNC have the same homotopy type.

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