English

The combinatorial cost

Group Theory 2007-05-23 v1 Combinatorics

Abstract

We study the combinatorial analogues of the classical invariants of measurable equivalence relations. We introduce the notion of cost and β\beta-invariants (the analogue of the first L2L^2-Betti number introduced by Gaboriau) for sequences of finite graphs with uniformly bounded vertex degrees and examine the relation of these invariants and the rank gradient resp. mod pp homology gradient invariants introduced by Lackenby for residually finite groups.

Keywords

Cite

@article{arxiv.math/0608474,
  title  = {The combinatorial cost},
  author = {Gábor Elek},
  journal= {arXiv preprint arXiv:math/0608474},
  year   = {2007}
}