The collars of a Riemannian manifold and stable isosystolic inequalities
The collars of a Riemannian manifold and stable isosystolic inequalities
We define the p-dimensional collar Col p (M,g) of a compact torsion-free Riemannian manifold (M, g) to be the greatest lower bound of the masses of all the /7-dimensional currents which represent non-trivial integral homology classes.When the cohomology ring of M satisfies a certain non-degeneracy condition there is an inequality …