Higher connectedness of asymptotic cones

TR Riley

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)

Abstract

We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions concerning filling N-spheres in an appropriate coarse sense. We interpret the criteria in the case where X is a finitely generated group Gamma with a word metric. This leads to upper bounds on filling functions for groups with simply connected cones-in particular they have linearly bounded filling length functions. We prove that if all the asymptotic cones of Gamma are N-connected then Gamma is of type FN+1 and we provide Nth order isoperimetric and isodiametric functions. Also we show that the asymptotic cones of a virtually polycyclic group Gamma are all contractible if and only if Gamma is virtually nilpotent.
Translated title of the contributionHigher connectedness of asymptotic cones
Original languageEnglish
Pages (from-to)1289 - 1352
Number of pages64
JournalTopology
Volume42 (6)
DOIs
Publication statusPublished - Nov 2003

Bibliographical note

Publisher: Elsevier

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