Regularity theorem for totally nonnegative flag varieties

Abstract

We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the closure of each positroid cell inside the totally nonnegative Grassmannian is homeomorphic to a ball, confirming a conjecture of Postnikov.

arXiv comment63 pages, 2 figures; v2: Minor changes; v3: Final version to appear in J. Amer. Math. Soc

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Cited by in corpus (12)

• Moment curves and cyclic symmetry for positive Grassmannians
• On two notions of total positivity for partial flag varieties
• Critical varieties in the Grassmannian
• Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties
• Cyclic symmetry loci in Grasssmannians
• Spaces of Lorentzian and real stable polynomials are Euclidean balls
• The Moduli Space of Harnack Curves in Toric Surfaces
• Shelling the m=1 amplituhedron
• A Kazhdan-Lusztig Atlas on G/P
• Boundary measurement and sign variation in real projective space
• Wronskians, total positivity, and real Schubert calculus
• Flag manifolds over semifields