Duke Mathematical Journal

Torsion homology growth and cycle complexity of arithmetic manifolds

Nicolas Bergeron, Mehmet Haluk Şengün, and Akshay Venkatesh

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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 we give evidence for this. We explain the relationship between this conjecture and the study of torsion homology growth.

Article information

Duke Math. J. Volume 165, Number 9 (2016), 1629-1693.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 57M50: Geometric structures on low-dimensional manifolds

hyperbolic geometry modular forms cycle complexity


Bergeron, Nicolas; Şengün, Mehmet Haluk; Venkatesh, Akshay. Torsion homology growth and cycle complexity of arithmetic manifolds. Duke Math. J. 165 (2016), no. 9, 1629--1693. doi:10.1215/00127094-3450429. https://projecteuclid.org/euclid.dmj/1456150040

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