Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexes

Key Points

• Borel asymptotic dimension is shown to be bounded from above by the dimension in these complexes.
• The study highlights the relationship between the structure of finite dimensional CAT(0) cube complexes and their Borel median graphs.
• The Roller compactification provides a significant framework in understanding these dimensions in the context of geometry.
• This finding suggests that Borel asymptotic dimension behaves predictively in the context of cube complexes.