Year: 2006
Type: preprint
Abstract: We study the combinatorial analogues of the classical invariants of measurable equivalence relations. We introduce the notion of cost and $β$-invariants (the analogue of the first $L^2$-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 $p$ homology gradient invariants introduced by Lackenby for residually finite groups.
Source: arXiv (Cornell University)
Author: Elek, Gábor
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1612339770