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Separable and tree-like asymptotic cones of groups

Using methods from nonstandard analysis, we will discuss which metric spaces can be realized as ultralimits (in particular, asymptotic cones). For example, we will show that any separable ultralimit is proper. Applying the results we will find in the context of groups, we will classify the real trees appearing as asymptotic cones of (not necessarily hyperbolic) finitely generated groups. Also, we show that all proper metric spaces can be realized as asymptotic cones.

Titel: Separable and tree-like asymptotic cones of groups
Verfasser: Sisto, Alessandro GND
Organisation: FB 10: Mathematik und Informatik
Dokumenttyp: Artikel
Medientyp: Text
Erscheinungsdatum: 2012
Publikation in MIAMI: 23.10.2012
Datum der letzten Änderung: 07.05.2015
Zeitschrift/Periodikum: Münster Journal of Mathematics / 5 (2012), S. 233 - 248
Fachgebiete: Mathematik
Sprache: Englisch
Format: PDF-Dokument
URN: urn:nbn:de:hbz:6-88399586094
Permalink: https://nbn-resolving.org/urn:nbn:de:hbz:6-88399586094
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