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Torsion homology growth and cycle complexity of arithmetic manifolds

2016; Duke University Press; Volume: 165; Issue: 9 Linguagem: Inglês

10.1215/00127094-3450429

1547-7398

Nicolas Bergeron, Mehmet Haluk Şengün, Akshay Venkatesh,

Topological and Geometric Data Analysis

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.