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arXiv · 1401.6989

Torsion homology growth and cycle complexity of arithmetic manifolds

Nicolas Bergeron·Mehmet Haluk Sengun·Akshay Venkatesh
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Abstract

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.

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Nicolas Bergeron, Mehmet Haluk Sengun, Akshay Venkatesh. 2014-01-27. Torsion homology growth and cycle complexity of arithmetic manifolds. https://doi.org/10.1215/00127094-3450429

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