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This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.
On the local structure and the homology of CAT$(\kappa)$ spaces and euclidean buildings
local structure CAT$(\kappa)$ spaces euclidean buildings
2010/12/7
We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional ...
Generalized triangle inequalities in thick Euclidean buildings of rank 2
Generalized triangle inequalities thick Euclidean buildings of rank 2
2010/12/1
We give the generalized triangle inequalities which determine the possible -valued side lengths of n-gons in thick Euclidean buildings of rank 2.