The amplituhedron crossing and winding numbers

Xavier Blot (Korresp. Autor*in), Jianrong Li

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed


In [2], Arkani-Hamed, Thomas and Trnka formulated two conjectural descriptions of the tree amplituhedron A n,k,m depending on the parity of m. When m is even, the description involves the winding number and when m is odd the description involves the crossing number. In this paper, we prove that if a point of the amplituhedron is in the image of the positive Grassmannian by the amplituhedron map, then it satisfies the winding or crossing descriptions depending on the parity of m. When m=2, we also prove that the other direction: a point satisfying the winding description is inside the amplituhedron.

FachzeitschriftJournal of Geometry and Physics
PublikationsstatusVeröffentlicht - Nov. 2023

ÖFOS 2012

  • 101001 Algebra