201401.6989v1 Torsion homology growth and cycle complexity of arithmetic manifolds

Let M be an arithmetic hyperbolic 3-manifold, such as a Bianchi manifold. We conjecture that there is a basis for the second homology of M, where each basis element is represented by a surface of `low´ genus, and give evidence for this. We explain the relationship between this conjecture and the study of torsion homology growth.