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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