Quasi-isometric rigidity of non-cocompact S-arithmetic lattices
نویسنده
چکیده
Throughout we let K be an algebraic number field, VK the set of all inequivalent valuations on K, and V ∞ K ⊆ VK the subset of archimedean valuations. We will use S to denote a finite subset of VK that contains V ∞ K , and we write the corresponding ring of S-integers in K as OS. In this paper, G will always be a connected non-commutative absolutely simple algebraic K-group. Any group of the form G(OS) is called an Sarithmetic group. For example, if m ∈ N, then PGLn(Z[1/m]) is an Sarithmetic group. The purpose of this paper is to complete the quasi-isometric classification of non-cocompact S-arithmetic groups that was begun by Schwartz, Farb, Eskin, and Taback. This is the final step in classifying up to quasi-isometry all of the lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic 0. Specifically, we show:
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