Axioms of affine buildings

TL;DR

This paper establishes the equivalence of various axiom sets defining affine buildings, provides a combinatorial proof for the existence of spherical buildings at infinity, and shows that the affine building property is independent of the metric structure.

Contribution

It offers a new combinatorial proof for the existence of spherical buildings at infinity and demonstrates the metric independence of affine building axioms.

Findings

Axiom sets for affine buildings are equivalent.

Existence of spherical buildings at infinity is proven combinatorially.

Affine building property is independent of metric structure.

Abstract

We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that ``being an affine building'' is independent of the metric structure of the space.