Regular Article
There Is No Tame Triangulation of the Infinite Real Grassmannian

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Abstract

We show that there is no triangulation of the infinite real Grassmannian G(k, R) nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of G(k, R) 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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Both authors partially supported by grants from the National Science Foundation.