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15 June 2016 Torsion homology growth and cycle complexity of arithmetic manifolds
Nicolas Bergeron, Mehmet Haluk Şengün, Akshay Venkatesh
Duke Math. J. 165(9): 1629-1693 (15 June 2016). DOI: 10.1215/00127094-3450429

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 we 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 Şengün. Akshay Venkatesh. "Torsion homology growth and cycle complexity of arithmetic manifolds." Duke Math. J. 165 (9) 1629 - 1693, 15 June 2016. https://doi.org/10.1215/00127094-3450429

Information

Received: 30 January 2014; Revised: 24 August 2015; Published: 15 June 2016
First available in Project Euclid: 22 February 2016

zbMATH: 1351.11031
MathSciNet: MR3513571
Digital Object Identifier: 10.1215/00127094-3450429

Subjects:
Primary: 11F67
Secondary: 57M50

Keywords: cycle complexity , hyperbolic geometry , modular forms

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 9 • 15 June 2016
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