For higher-rank locally symmetric spaces and affine buildings, generator number and logarithmic first-homology torsion grow sublinearly in volume when the injectivity radius is large or along Benjamini-Schramm convergent sequences.
On the growth ofL2-invariants for sequences of lattices in Lie groups.Ann
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Sparse Random Covers and Growth of Torsion in First Homology
For higher-rank locally symmetric spaces and affine buildings, generator number and logarithmic first-homology torsion grow sublinearly in volume when the injectivity radius is large or along Benjamini-Schramm convergent sequences.