Trees, Ultrametrics, and Noncommutative Geometry
Trees, Ultrametrics, and Noncommutative Geometry
Noncommutative geometry is used to study the local geometry of ultrametric spaces and the geometry of trees at infinity.Connes's example of the noncommutative space of Penrose tilings is interpreted as a non-Hausdorff orbit space of a compact, ultrametric space under the action of its local isometry group.This is generalized to …