Abért, Miklós and Gelander, T. and Nikolov, N. (2017) Rank, combinatorial cost, and homology torsion growth in higher rank lattices. DUKE MATHEMATICAL JOURNAL, 166 (15). pp. 29252964. ISSN 00127094

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Abstract
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 rightangled 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 nonuniform lattices in higher rank simple Lie groups are right angled. We provide the first examples of uniform (cocompact) rightangled arithmetic groups in SL(n,ℝ), n ≥ 3, and 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. By 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 rightangled lattice in a higher rank simple Lie group. © 2017.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  12 Feb 2018 07:37 
Last Modified:  12 Feb 2018 07:37 
URI:  http://real.mtak.hu/id/eprint/74284 
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