Filling Invariants at Infinity and the Euclidean Rank of Hadamard Spaces
چکیده
In this paper we study a homological version of the asymptotic filling invariant divk defined by Brady and Farb in [BrFa] and show that it is a quasi-isometry invariant for all proper cocompact Hadamard spaces, i.e. proper cocompact CAT(0)-spaces, and that it can furthermore be used to detect the Euclidean rank of such spaces. We thereby extend results of [BrFa, Leu, Hin] from the setting of symmetric spaces of non-compact type to that of Hadamard spaces. Finally, we exhibit the optimal growth of the k-th homological divergence for symmetric spaces of non-compact type with Euclidean rank no larger than k and for CAT(κ)-spaces with κ < 0.