Speaker: Michael Dobbins, Binghamton University

Title: Grassmannians and Pseudosphere Arrangements

Abstract: I will present an extension of vector configurations to more general objects that have nicer combinatorial and topological properties, namely weighted pseudosphere arrangements, as in the topological representation theorem of oriented matroids. These form a metric space, and in rank 3, are homotopy equivalent to the corresponding Grassmannians. Also, the subspaces representing a fixed oriented matroid are contractible. This is a sharp contrast with vector configurations where the space of realizations can have the homotopy type of any primary semialgebraic set even in rank 3. Work on these spaces was partly motivated by combinatorial tools for working with vector bundles.

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