The universality theorem for neighborly polytopes

Abstract

In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of a neighborly simplicial polytope. This in particular provides the final step for Mnëv‘s proof of the universality theorem for simplicial polytopes.

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Correspondence to Karim A. Adiprasito.

Additional information

K. A. Adiprasito acknowledges support by an EPDI postdoctoral fellowship and by the Romanian NASR, CNCS — UEFISCDI, project PN-II-ID-PCE-2011-3-0533. The research of A. Padrol was supported by the DFG Collaborative Research Center SFB/TR 109 “Discretization in Geometry and Dynamics”.

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Adiprasito, K.A., Padrol, A. The universality theorem for neighborly polytopes. Combinatorica 37, 129–136 (2017). https://doi.org/10.1007/s00493-016-3253-9

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Mathematics Subject Classification (2000)

  • 52B40
  • 52C40
  • 14P10