(JOINT DISCRETE MATH & TOPOLOGY SEMINAR)

Grassmanians and Pseudosphere Arrangements

Michael Dobbins

Department of Mathematics, Binghamton University, Binghamton, NY, USA

Department of Mathematics, Binghamton University, Binghamton, NY, USA

2018/5/

**30**Wednesday 5PMIn 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.