Realization Spaces of Arrangements of Convex Bodies

  title={Realization Spaces of Arrangements of Convex Bodies},
  author={Michael Gene Dobbins and Andreas F. Holmsen and Alfredo Hubard},
  journal={Discrete \& Computational Geometry},
We introduce combinatorial types of planar arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial complexity of the bodies and the topological complexity of their realization space. First, we show that every combinatorial type is realizable and its realization space is contractible under mild assumptions. Second, we prove a universality theorem that… 

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Grassmannians and pseudosphere arrangements

  • M. G. Dobbins
  • Mathematics
    Journal de l’École polytechnique — Mathématiques
  • 2021
We extend vector configurations to more general objects that have nicer combinatorial and topological properties, called weighted pseudosphere arrangements. These are defined as a weighted variant of

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On the Combinatorial Classification of Nondegenerate Configurations in the Plane