UNIVERSAL TREE-GRADED SPACES AND ASYMPTOTIC CONES
UNIVERSAL TREE-GRADED SPACES AND ASYMPTOTIC CONES
We define and give explicit construction of a universal tree-graded space with a given collection of pieces. We apply that to proving uniqueness of asymptotic cones of relatively hyperbolic groups whose peripheral subgroups have unique asymptotic cones. Modulo the Continuum Hypothesis, we show that if an asymptotic cone of a …