In 1983 Gromov proved the systolic inequality: if M is a closed, essential n-dimensional Riemannian manifold where every loop of length 2 is null-homotopic, then the volume of M is at least a constant depending only on n. He also proved a version that depends on the simplicial volume of M, a topological invariant generalizing the hyperbolic volume of a closed hyperbolic manifold. If the simplicial volume is large, then the lower bound on volume becomes proportional to the simplicial volume divided by the n-th power of its logarithm. Nabutovsky showed in 2019 that Papasoglu's method of area-minimizing separating sets recovers the systolic inequality and improves its dependence on n. We introduce simplicial volume to the proof, recovering the statement that the volume is at least proportional to the square root of the simplicial volume.
