The totally nonnegative Grassmannian is a ball

Abstract

We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, the compactification of the space of electrical networks, and the cyclically symmetric amplituhedron.

19 pages. v2: Exposition improved in many places. v3: Final version

References in corpus (5)

• Total positivity, Grassmannians, and networks
• The m=1 amplituhedron and cyclic hyperplane arrangements
• The totally nonnegative part of G/P is a ball
• Moment curves and cyclic symmetry for positive Grassmannians
• Combinatorial formulas for Le-coordinates in a totally nonnegative Grassmannian

Cited by in corpus (14)

• Regularity theorem for totally nonnegative flag varieties
• The Two-Loop Remainder Function for Eight and Nine Particles
• Boundaries of the Amplituhedron with amplituhedronBoundaries
• The totally nonnegative part of G/P is a ball
• Moment curves and cyclic symmetry for positive Grassmannians
• On the Uniqueness of Co-circular Four Body Central Configurations
• Critical varieties in the Grassmannian
• Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties
• Cyclic symmetry loci in Grasssmannians
• The Amplituhedron BCFW Triangulation
• Spaces of Lorentzian and real stable polynomials are Euclidean balls
• Fibers of maps to totally nonnegative spaces
• Shelling the m=1 amplituhedron
• Boundary measurement and sign variation in real projective space