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Gromov's universal filling inequalities relate the filling radius and thefilling volume of a Riemannian manifold to its volume. The main result of thepresent article is that in dimensions at least three the optimal constants inthe filling inequalities depend only on dimension and orientability, not on themanifold itself. This contrasts with the analogous situation for the optimalsystolic inequality, which does depend on the manifold.

Filling inequalities do not depend on topology