We say that a graph G is Local-to-Global rigid if there exists R>0 such that every other graph whose balls of radius R are isometric to the balls of radius R in G is covered by G. Examples include the Euclidean building of PSLn(Qp). We show that the rigidity of the building goes further by proving that a reconstruction is possible from only a partial local information, called “print”. We use this to prove the rigidity of graphs quasi-isometric to the building among which are the torsion-free lattices of PSLn(Qp).
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- Junior Topology and Group Theory Seminar