Duke Mathematical Journal

Torsion homology growth and cycle complexity of arithmetic manifolds

Nicolas Bergeron, Mehmet Haluk Şengün, and 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 we give evidence for this. We explain the relationship between this conjecture and the study of torsion homology growth.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1456150040

Digital Object Identifier
doi:10.1215/00127094-3450429

Mathematical Reviews number (MathSciNet)
MR3513571

Zentralblatt MATH identifier
1351.11031

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

Keywords
hyperbolic geometry modular forms cycle complexity

Citation

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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