Torsion homology growth and cycle complexity of arithmetic manifolds

Nicolas Bergeron, Mehmet Haluk Şengün, Akshay Venkatesh
2016 Duke mathematical journal  
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.
doi:10.1215/00127094-3450429 fatcat:hjo24jrmozfn5kkbwxhpoafjxe