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A quantitative bounded distance theorem and a Margulis’ lemma for $\mathbb Z^n$-actions, with applications to homology
We consider the stable norm associated to a discrete, torsionless abelian group of isometries \Gamma \cong \mathbb Z^n of a geodesic space (X,d) . We show that the difference between the stable norm \| \;\, \|_{\mathrm {st}} and the distance d is bounded by a constant only depending on the …