English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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.

Filling invariants at infinity and the Euclidean rank of Hadamard spaces