Strong systolic freedom of closed manifolds end of polyhedrons

Systols of dimension k for a Riemannian manifold of dimension n were introduced by M. Berger in 1972. The problem of intersystolic freedom (or (k, n - k) - freedom) deals with the supremum of the product of two supplementary dimensional systols, say k and n - k, when metric of M runs in the class of metrics with unit volume. Intersystolic freedom means that this supremum is equal to infinity. A few partial results in this direction were recently obtained by M. Katz, A. Suciu and the author. In the article we present a general theorem about the strong intersystolic freedom of arbitrary Riemannian polyhedrons. This result implies in particular the intersystolic freedom for any closed manifold.