  We investigate the rank gradient and growth of torsion in homology in
residually finite groups. As a tool, we introduce a new complexity notion for
generating sets, using measured groupoids and combinatorial cost.
  As an application we prove the vanishing of the above invariants for Farber
sequences of subgroups of right angled groups. A group is right angled if it
can be generated by a sequence of elements of infinite order such that any two
consecutive elements commute.
  Most non-uniform lattices in higher rank simple Lie groups are right angled.
We provide the first examples of uniform (co-compact) right angled arithmetic
groups in $\mathrm{SL}(n,\mathbb{R}),~n\geq 3$ and $\mathrm{SO}(p,q)$ for some
values of $p,q$. This is a class of lattices for which the Congruence Subgroup
Property is not known in general.
  Using rigidity theory and the notion of invariant random subgroups it follows
that both the rank gradient and the homology torsion growth vanish for an
arbitrary sequence of subgroups in any right angled lattice in a higher rank
simple Lie group.
