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.

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

References in corpus (4)

• Double Bruhat Cells in Kac-Moody Groups and Integrable Systems
• CW posets after the Poincare Conjecture
• Fibers of maps to totally nonnegative spaces
• A Kazhdan-Lusztig Atlas on G/P

Cited by in corpus (10)

• Critical varieties in the Grassmannian
• On two notions of total positivity for partial flag varieties
• 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
• A Kazhdan-Lusztig Atlas on G/P
• Shelling the m=1 amplituhedron
• Wronskians, total positivity, and real Schubert calculus
• Flag manifolds over semifields
• Boundary measurement and sign variation in real projective space