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Farber’s conjecture for planar graphs

    1. [1] Northeastern University

      Northeastern University

      City of Boston, Estados Unidos

  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 5, 2021
  • Idioma: inglés
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  • Resumen
    • We prove that the ordered configuration spaces of planar graphs have the highest possible topological complexity generically, as predicted by a conjecture of Farber. Our argument establishes the same generic maximality for all higher topological complexities. We include some discussion of the non-planar case, demonstrating that the standard approach to the conjecture fails at a fundamental level.


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