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Topological median structures on R^n

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OGGW02 - Actions on graphs and metric spaces

A topological median structure on a topological space X is acontinuous map m:X3->X satisfying certain axioms. A CAT cube complex X has a natural median structure, where m(a,b,c) is theunique point that belongs to three l1-gedesics that connect each pairab, ac, bc. In a work in progress, joint with Ken Bromberg and MichahSageev, we show that median structures on R^n are locally induced bycubulations of neighborhoods. The proof is by induction on n, andrequires us to prove the same theorem for ER homology manifolds.

This talk is part of the Isaac Newton Institute Seminar Series series.

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