Nested Affine Buildings and Their Group Decompositions

TL;DR

This paper introduces Babel buildings, a new higher-dimensional generalization of affine buildings, providing a novel framework for analyzing group actions on complex non-positive curvature spaces.

Contribution

The paper constructs Babel buildings, expanding the theory of affine buildings and offering new tools for understanding group decompositions in non-standard geometric settings.

Findings

Babel buildings are non-connected, non-convex metric spaces with non-positive curvature.

They facilitate the study of group actions in complex geometric contexts.

Key results include metric and nesting structure analyses of Babel buildings.

Abstract

In this paper, we construct a higher dimensional generalization of affine buildings and introduce a new structure, which we call Babel buildings. These buildings are non-connected, non-convex metric spaces of non-positive curvature. Despite their non-standard properties, Babel buildings provide an effective framework for studying the structure of groups acting on them. We analyze the metric and nesting structures of Babel buildings and derive key results regarding the group actions consistent with this new framework.