Totally nonnegative critical varieties

Abstract

We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit${}_f^{\ge 0}$ is the image of an affine poset cyclohedron under a continuous map and use this map to define a boundary stratification of Crit${}_f^{\ge 0}$. For the case of the top-dimensional positroid cell, we show that the totally nonnegative critical variety Crit${}_{k,n}^{\ge 0}$ is homeomorphic to the second hypersimplex ${\Delta }_{2,n}$.

arXiv comment31 pages, 11 figures. Final version to appear in IMRN