Boundary measurement and sign variation in real projective space
arXiv:1909.04640 · doi:10.4171/AIHPD/125
Abstract
We define two generalizations of the totally nonnegative Grassmannian and determine their topology in the case of real projective space. We find the spaces to be PL manifolds with boundary which are homotopy equivalent to another real projective space of smaller dimension. One generalization makes use of sign variation while the other uses boundary measurement. Spaces arising from boundary measurement are shown to admit Cohen-Macaulay triangulations.
v2 contains corrections of minor typos and is the accepted version to appear in Ann. Inst. Henri Poincaré D