There is no tame triangulation of the infinite real Grassmannian
Laura Anderson, James F. Davis
Abstract
We show that there is no triangulation of the infinite real Grassmannian of k-planes in R∞ which is nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of the Grassmannian subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane.
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