4 research outputs found
On axiomatic definitions of non-discrete affine buildings
In this paper we prove equivalence of sets of axioms for non-discrete affine
buildings, by providing different types of metric, exchange and atlas
conditions. We apply our result to show that the definition of a Euclidean
building depends only on the topological equivalence class of the metric on the
model space. The sharpness of the axioms dealing with metric conditions is
illustrated in an appendix. There it is shown that a space X defined over a
model space with metric d is possibly a building only if the induced distance
function on X satisfies the triangle inequality.Comment: Errors corrected, results extended. (This replaces the two earlier,
separate preprints "Axioms of affine buidlings" arXiv:0909.2967v1 and "Affine
buildings II" arXiv:0909.2059v1.
\Lambda-buildings and base change functors
We prove an analog of the base change functor of \Lambda-trees in the setting
of generalized affine buildings. The proof is mainly based on local and global
combinatorics of the associated spherical buildings. As an application we
obtain that the class of generalized affine building is closed under ultracones
and asymptotic cones. Other applications involve a complex of groups
decompositions and fixed point theorems for certain classes of generalized
affine buildings.Comment: revised version, 29 pages, to appear in Geom. Dedicat