The totally nonnegative Grassmannian is a ball
Throughout the semester, we have explored some aspects of polytopes and other spaces that exhibit a positive geometry. One space that we have seen is a positive geometry is the totally nonnegative Grassmannian, but it is not a polytope. However, like a polytope, the totally nonnegative Grassmannian is a regular CW complex homeomorphic to a closed ball, which was conjectured by Postnikov and proven by Galashin-Karp-Lam. In this talk, we will give a different, self-contained argument, also due to Galashin-Karp-Lam, that the totally nonnegative Grassmannian is homeomorphic to a closed ball. To do so, we will exhibit a homeomorphism by constructing a contractive flow on the totally nonnegative Grassmannian.
Date published: Wednesday, October 25, 2023