  In this paper, we prove that the systolic volume of a closed aspherical
3-manifold is bounded below in terms of complexity. Systolic volume is defined
as the optimal constant in a systolic inequality. Babenko showed that the
systolic volume is a homotopy invariant. Moreover, Gromov proved that the
systolic volume depends on topology of the manifold. More precisely, Gromov
proved that the systolic volume is related to some topological invariants
measuring complicatedness. In this paper, we work along Gromov's spirit to show
that systolic volume of 3-manifolds is related to complexity. The complexity of
3-manifolds is the minimum number of tetrahedra in a triangulation, which is a
natural tool to evaluate the combinatorial complicatedness.

Geometric Topology