Cantor combinatorics and almost finiteness

Abstract

In this survey we give a concise introduction to a continuous version of Borel combinatorics. Our approach will have a certain algorithm-theoretic nature and we will give special emphasis to the notion of almost finiteness introduced by Matui as a continuous analogue of Borel hyperfiniteness. We also show how the theory can be used to study spectral convergence for graph Laplacians.