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Bibliographic Metadata

  • Title
    Separable and tree-like asymptotic cones of groups
  • Author
    Sisto, Alessandro
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 233-248
  • Published
    2012
  • Language
    English
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-88399586094 
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Abstract
  • 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.
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