Title: Family of hyperbolic manifolds with exponential homology torsion growth
Abstract: We discuss a recent construction of a family of compact hyperbolic manifolds whose homology torsion grows exponentially with respect to volume. This shows that the upper bounds on torsion growth obtained by Bader, Gelander, and Sauer are asymptotically sharp.
The construction is based on arithmetic hyperbolic manifolds of simplest type and uses right-angled Coxeter groups together with retraction techniques inspired by Bergeron–Haglund–Wise. A key ingredient is the existence of sufficiently many “independent” totally geodesic submanifolds, which produce large torsion in homology.
We outline the main ideas of the construction and discuss the geometric mechanisms behind exponential torsion growth.
Michael Zshornack
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