Topology of Geometric Joins

@article{Brny2015TopologyOG,
  title={Topology of Geometric Joins},
  author={Imre B{\'a}r{\'a}ny and Andreas F. Holmsen and Roman N. Karasev},
  journal={Discrete & Computational Geometry},
  year={2015},
  volume={53},
  pages={402-413}
}
  • Imre Bárány, Andreas F. Holmsen, Roman N. Karasev
  • Published 2015
  • Computer Science, Mathematics
  • Discrete & Computational Geometry
  • We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carathéodory and Tverberg theorems, and their relatives. We conjecture that when the family has at least $$d+1$$d+1 sets, where $$d$$d is the dimension of the space, then the geometric join is contractible. We are able to prove this when $$d$$d equals $$2$$2 and $$3$$3, while for larger $$d$$d we show that the geometric join is contractible provided the number… CONTINUE READING

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