Torsion homology growth and cycle complexity of arithmetic manifolds

By Nicolas Bergeron, Mehmet Haluk Sengun, Akshay Venkatesh. Duke mathematical journal, 2014

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8e00bfd5fa2575f3015a4efa98a003dac6617af1