The universality theorem for neighborly polytopes

Combinatorica volume 37, pages129–136(2017)Cite this article

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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Author information

Affiliations

  1. Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    Karim A. Adiprasito

  2. Institut de Mathématiques de Jussieu - Paris Rive Gauche, Universit Pierre et Marie Curie (Paris 06), Paris, France

    Arnau Padrol

Authors
  1. Karim A. Adiprasito
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  2. Arnau Padrol
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Corresponding author

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