\Lambda-buildings and base change functors

TL;DR

This paper extends the concept of base change functors from bb-trees to generalized affine buildings, using combinatorial methods, and demonstrates their stability under ultraconstructions with applications to decompositions and fixed point theorems.

Contribution

It introduces a new base change functor for generalized affine buildings and proves their closure properties under ultracones and asymptotic cones.

Findings

Generalized affine buildings are closed under ultracones and asymptotic cones.

The proof relies on combinatorics of spherical buildings.

Applications include decompositions and fixed point theorems.

Abstract

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.