4 papers · 1 filter
Sparse Random Covers and Growth of Torsion in First Homology
Raz Slutsky
We construct random open covers of higher-rank locally symmetric spaces using a construction we call scaffolded Poisson processes. Let be a symmetric space of noncompact ty…
A Product-Neighbourhood Criterion for Fixed Price One
Raz Slutsky
We prove a flexible criterion for fixed price one, applying in particular to higher-rank lattices over local fields and automorphism groups of affine buildings, including lattices…
On the Asymptotic Number of Generators of High Rank Arithmetic Lattices
Alexander Lubotzky, Raz Slutsky
Abert, Gelander and Nikolov [AGN17] conjectured that the number of generators of a lattice in a high rank simple Lie group grows sub-linearly with ,…
On the Minimal Size of a Generating Set of Lattices in Lie Groups
Tsachik Gelander, Raz Slutsky
We prove that the rank (that is, the minimal size of a generating set) of lattices in a general connected Lie group is bounded by the co-volume of the projection of the lattice to…