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A geodesic metric space is called tree-graded space, with respect to a collection of connected proper subsets called pieces, if any two distinct pieces intersect by at most one point, and every non-trivial simple geodesic triangle of is contained in one of the pieces. Thus, for pieces of bounded diameter, tree-graded spaces behave like real trees in their coarse geometry (in the sense of Gromov), while allowing non-tree-like behavior within the pieces. Tree-graded spaces were introduced by Cornelia Druţu and Mark Sapir in their study of the asymptotic cones of hyperbolic groups.

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dbo:abstract
  • A geodesic metric space is called tree-graded space, with respect to a collection of connected proper subsets called pieces, if any two distinct pieces intersect by at most one point, and every non-trivial simple geodesic triangle of is contained in one of the pieces. Thus, for pieces of bounded diameter, tree-graded spaces behave like real trees in their coarse geometry (in the sense of Gromov), while allowing non-tree-like behavior within the pieces. Tree-graded spaces were introduced by Cornelia Druţu and Mark Sapir in their study of the asymptotic cones of hyperbolic groups. (en)
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  • 8234367 (xsd:integer)
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  • 1427 (xsd:nonNegativeInteger)
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  • 891275549 (xsd:integer)
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dbp:author1Link
  • Cornelia Druţu (en)
dbp:author2Link
  • Mark Sapir (en)
dbp:first
  • Mark (en)
  • Cornelia (en)
dbp:last
  • Sapir (en)
  • Druţu (en)
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dbp:year
  • 2005 (xsd:integer)
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  • A geodesic metric space is called tree-graded space, with respect to a collection of connected proper subsets called pieces, if any two distinct pieces intersect by at most one point, and every non-trivial simple geodesic triangle of is contained in one of the pieces. Thus, for pieces of bounded diameter, tree-graded spaces behave like real trees in their coarse geometry (in the sense of Gromov), while allowing non-tree-like behavior within the pieces. Tree-graded spaces were introduced by Cornelia Druţu and Mark Sapir in their study of the asymptotic cones of hyperbolic groups. (en)
rdfs:label
  • Tree-graded space (en)
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