Systolic volume and complexity of 3manifolds
Abstract
In this paper, we prove that the systolic volume of a closed aspherical 3manifold 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 3manifolds is related to complexity. The complexity of 3manifolds is the minimum number of tetrahedra in a triangulation, which is a natural tool to evaluate the combinatorial complicatedness.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 arXiv:
 arXiv:1509.07647
 Bibcode:
 2015arXiv150907647C
 Keywords:

 Mathematics  Geometric Topology;
 53C23 (primary);
 57M27 (secondary)
 EPrint:
 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