Collapsible polyhedra and median spaces
نویسندگان
چکیده
منابع مشابه
Collapsible Polyhedra and Median Spaces
It is shown that a collapsible, compact, connected, simplicial polyhedron admits a cubical subdivision and a median convexity, such that all cubes are convex subspaces with a convexity of subcubes. Conversely, a compact, connected, cubical polyhedron with a convexity as described admits a collapsible simplicial subdivision. Such a convexity, when it exists, is uniquely determined by the corresp...
متن کاملMedian Spaces and Spaces with Measured Walls
We prove the existence of a close connection between spaces with measured walls and median metric spaces. In particular we show that some spaces with measured walls (e.g. real hyperbolic spaces) embed into median metric spaces which are at finite Hausdorff distance from their embedded image. We also relate properties (T) and Haagerup (a-T-menability) to actions on median spaces and on spaces wi...
متن کاملCoarse 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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We construct the first explicit example of a simplicial 3-ball B15,66 that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B12,38 with 12 vertices that is collapsible and not shellable, but evasive. Finally, we present the first explicit triangulation of a 3-sphere S18,125 (with only 18 vertices) that is not locally constructible. All these examples are based on knotted ...
متن کاملGroup Actions on Median Spaces
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan’s property (T) and Haagerup’s property.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04413-x