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Totally nonnegative critical varieties (2110.08548v2)
Published 16 Oct 2021 in math.AG, math-ph, math.CO, and math.MP
Abstract: We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit${\ge0}_f$ is the image of an affine poset cyclohedron under a continuous map and use this map to define a boundary stratification of Crit${\ge0}_f$. For the case of the top-dimensional positroid cell, we show that the totally nonnegative critical variety Crit${\ge0}_{k,n}$ is homeomorphic to the second hypersimplex $\Delta_{2,n}$.