Tri-partition of and hole systems in a polyhedral complex

  • Date:

    11.06.2019

  • 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.

  • Place:

    1.067 (20.30)