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. 
Nicolas Bergeron, Mehmet Haluk Sengun, Akshay Venkatesh
math.NT math.GT