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dc.contributor.author
Lang, Urs
dc.date.accessioned
2017-06-09T18:26:20Z
dc.date.available
2017-06-09T18:26:20Z
dc.date.issued
2011-07-29
dc.identifier.uri
http://hdl.handle.net/20.500.11850/44183
dc.description.abstract
Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. Isbell showed that every metric space X has an injective hull E(X). We prove that if X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E(X) is a locally finite polyhedral complex with finitely many isometry types of n-cells, isometric to polytopes in l^n_\infty, for each n. This applies to a class of finitely generated groups \Gamma, including word hyperbolic and abelian groups, among others. Then \Gamma\ acts properly on E(\Gamma) by cellular isometries, and the first barycentric subdivision of E(\Gamma) is a model for the classifying space \underbar{E}\Gamma\ for proper actions. If \Gamma\ is word hyperbolic, E(\Gamma) is finite dimensional and the action is cocompact; the injective hull thus provides an alternative to the Rips complex, with some extra features.
dc.language.iso
en
dc.title
Injective hulls of certain discrete metric spaces and groups
dc.type
Working Paper
ethz.pages.start
arXiv:1107.5971v1
ethz.size
38 p.
ethz.notes
Submitted on 29 July 2011.
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03500 - Lang, Urs / Lang, Urs
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03500 - Lang, Urs / Lang, Urs
ethz.identifier.url
http://arxiv.org/abs/1107.5971
ethz.date.deposited
2017-06-09T18:26:39Z
ethz.source
ECIT
ethz.identifier.importid
imp59364ed6823e670554
ethz.ecitpid
pub:72981
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-19T01:36:11Z
ethz.rosetta.lastUpdated
2018-10-01T15:22:42Z
ethz.rosetta.versionExported
true
ethz.COinS
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