Coarse Separation of Coarse PD(n) spaces

TL;DR

This paper proves that in coarse Poincaré duality spaces, any subspace that coarsely separates the space must have an asymptotic dimension at least one less than the space's dimension.

Contribution

It establishes a lower bound on the asymptotic dimension of separating subspaces in coarse Poincaré duality spaces, linking separation properties to asymptotic dimension.

Findings

Subspace coarsely separating a coarse PD(n) space has asymptotic dimension ≥ n-1.

Provides a coarse geometric analogue of classical separation results.

Enhances understanding of the structure of coarse Poincaré duality spaces.

Abstract

We show that if a subspace $A$ of a coarse $PD(n)$ metric space $X$ coarsely separates it, then it must have asymptotic dimension at least $n-1$.