Filling inequalities do not depend on topology

Details Filling inequalities do not depend on topology Filling inequalities do not depend on topology

2007-06-19

arxiv.org/abs/0706.2790v3

Mathematics

Geometric Topology

13 pages. Corrected some minor errors. To appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal)

Scientific paper

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

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