Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 9 (2016), 1629-1693.
Torsion homology growth and cycle complexity of arithmetic manifolds
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.
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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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.