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- W2953231723 abstract "Let X be a building of arbitrary type. A compactification $C_r(X)$ of the set Res(X) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res(X) endowed with a natural combinatorial distance which we call the root-distance. Points of $C_r(X)$ admit amenable stabilisers in Aut(X) and conversely, any amenable subgroup virtually fixes a point in $C_r(X)$. In addition, it is shown that, provided Aut(X)is transitive enough, this compactification also coincides with the group-theoretic compactification constructed using the Chabauty topology on closed subgroups of Aut(X). This generalises to arbitrary buildings results established by Y. Guivarc'h and B. R'emy in the Bruhat--Tits case." @default.
- W2953231723 created "2019-06-27" @default.
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- W2953231723 date "2009-01-26" @default.
- W2953231723 modified "2023-10-16" @default.
- W2953231723 title "Combinatorial and group-theoretic compactifications of buildings" @default.
- W2953231723 hasPublicationYear "2009" @default.
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