Information-based complexity: Difference between revisions

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A [[geodesic]] [[metric space]] <math>X</math> is called '''''tree-graded space''''', with respect to a collection of connected proper subsets called ''pieces'', if any two distinct pieces [[Intersection (set theory)|intersect]] by at most one point, and every non-trivial simple geodesic [[triangle]] of <math>X</math> is contained in one of the pieces.
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Thus, for pieces of bounded [[diameter]], tree-graded spaces behave like [[real tree]]s in their [[Quasi-isometry|coarse geometry]] (in the sense of [[Mikhail Leonidovich Gromov|Gromov]]) while allowing non-tree-like behavior within the pieces.
 
Tree-graded spaces were introduced by {{harvtxt|Druţu|Sapir|2005}} in their study of the [[Ultralimit#Asymptotic cones|asymptotic cones]] of [[hyperbolic group]]s.
 
==References==
*{{citation
| last1 = Druţu | first1 = Cornelia | author1-link = Cornelia Druţu
| last2 = Sapir | first2 = Mark
| doi = 10.1016/j.top.2005.03.003
| issue = 5
| journal = Topology
| mr = 2153979
| pages = 959–1058
| title = Tree-graded spaces and asymptotic cones of groups
| volume = 44
| year = 2005}}.
 
{{DEFAULTSORT:Tree-Graded Space}}
[[Category:Metric geometry]]
[[Category:Trees (topology)]]
 
 
{{Geometry-stub}}

Latest revision as of 23:40, 8 October 2014

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