Geodesic
Boundary measurement and sign variation in real projective space
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 3, pp. 543-565.

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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.

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DOI : 10.4171/aihpd/125
Classification : 05-XX, 06-XX, 14-XX, 57-XX
Keywords: sign variation, totally nonnegative Grassmannian, PL manifold 
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     title = {Boundary measurement and sign variation in real projective space},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {543--565},
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     zbl = {1510.14035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/125/}
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Machacek, John. Boundary measurement and sign variation in real projective space. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 3, pp. 543-565. doi : 10.4171/aihpd/125. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/125/

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