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.
- Pub Date:
- September 2015
- Mathematics - Geometric Topology;
- 53C23 (primary);
- 57M27 (secondary)
- 18 pages. There is a substantial change in the update of the proof of the main theorem: new methods and techniques are added to replace the original arguments