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Tri-partition of and hole systems in a polyhedral complex

Tri-partition of and hole systems in a polyhedral complex
Date:

11.06.2019

Place:

1.067 (20.30)

Speaker:

Herbert Edelsbrunner

Time:

15:45-16:45

Source:

Tri-partition of and hole systems in a polyhedral complex

Abstract: We prove that for every polyhedral complex, K, and every dimension, p, there is a partition of the p-cells into a maximal p-tree, a maximal p-cotree, and the remaining p-cells defining the p-th homology of K. As an application, we consider the manipulation of the hole structure in geometric shapes, using the tri-partition to facilitate the opening and closing of holes. In a concrete application, we let K be the Delaunay mosaic of a finite set, and we extract a partial order on the filtration induced by the radius function, whose cuts define the subcomplexes that can be constructed with this method.

Joint work with Katharina Oelsboeck.