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Grassmanians and Pseudosphere Arrangements
[2018 Discrete Math 세미나]
Date: 2018-05-30
Speaker : Michael Dobbins (Binghamton University, Binghamton, NY, USA)
Abstract : In this talk I will present a metric space of pseudosphere arrangements, as in the topological representation theorem of oriented matroids, where each pseudosphere is assigned a weight. This gives an extension of the space of full rank vector configurations of fixed size in a fixed dimension that has nicer combinatorial and topological properties. In rank 3 these spaces, modulo SO(3), are homotopy equivalent to Grassmanians, and the subspaces representing a fixed oriented matroid are contractible. Work on these spaces was partly motivated by combinatorial tools for working with vector bundles.
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