Totally nonnegative critical varieties
Abstract
We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit0f is the image of an affine poset cyclohedron under a continuous map and use this map to define a boundary stratification of Crit0f. For the case of the top-dimensional positroid cell, we show that the totally nonnegative critical variety Crit0k,n is homeomorphic to the second hypersimplex 2,n.
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