Tree-graded space (original) (raw)
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.
| Property | Value |
|---|---|
| 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) |
| dbo:wikiPageID | 8234367 (xsd:integer) |
| dbo:wikiPageLength | 1427 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 891275549 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Hyperbolic_group dbr:Quasi-isometry dbr:Real_tree dbr:Geodesic dbr:Connected_space dbc:Trees_(topology) dbr:Intersection_(set_theory) dbc:Metric_geometry dbr:Topology_(journal) dbr:Triangle dbr:Diameter dbr:Metric_space dbr:Mikhail_Leonidovich_Gromov dbr:Ultralimit |
| dbp:author1Link | Cornelia Druţu (en) |
| dbp:author2Link | Mark Sapir (en) |
| dbp:first | Mark (en) Cornelia (en) |
| dbp:last | Sapir (en) Druţu (en) |
| dbp:wikiPageUsesTemplate | dbt:Citation dbt:Geometry-stub dbt:Harvs |
| dbp:year | 2005 (xsd:integer) |
| dct:subject | dbc:Trees_(topology) dbc:Metric_geometry |
| rdfs:comment | 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) |
| owl:sameAs | freebase:Tree-graded space wikidata:Tree-graded space https://global.dbpedia.org/id/4wt2F |
| prov:wasDerivedFrom | wikipedia-en:Tree-graded_space?oldid=891275549&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Tree-graded_space |
| is dbo:wikiPageWikiLink of | dbr:Cornelia_Druțu dbr:Real_tree |
| is foaf:primaryTopic of | wikipedia-en:Tree-graded_space |