Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals
نویسندگان
چکیده
منابع مشابه
Coarse Median Spaces and Groups
We introduce the notion of a coarse median on a metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of such a median on a geodesic space is quasi-isometry invariant, and so applies to finitely generated groups via their Cayley graphs. We show that asymptotic cones of such spaces are topological median algebras. We define a notion of rank for a coars...
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1 Introductory graph and metric notions 5 1.1 The Cheeger constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Expander graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Isoperimetric dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Rough isome...
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We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains.
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2021
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-021-00623-8