Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Systolic volume and complexity of 3-manifolds   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.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas