Fractional Abelian topological phases of matter for fermions in two-dimensional space

Abstract: These notes constitute chapter 7 from "l'Ecole de Physique des Houches" Session CIII, August 2014 dedicated to Topological Aspects of Condensed matter physics. The tenfold way in quasi-one-dimensional space is presented. The method of chiral Abelian bosonization is reviewed. It is then applied to the stability analysis for the edge theory in symmetry class AII, and for the construction of two-dimensional topological phases from coupled wires.