| Abstract: | Recently, topological phases of matter have been at the focus of condensed matter physics. I will focus on states stabilized by strong inter-particle interactions, refereed to as fractional topological states. These states are receiving much theoretical attention but have not been observed experimentally except in the form of the fractional quantum Hall effect. I will present a recently developed simple theoretical approach to these complicated states, known as the wire-construction approach. This new perspective allows to proceed all the way from the microscopic Hamiltonian of interacting particles, e.g. in a magnetic field or in the presence of spin-orbit coupling, and end up with the underlying properties characterizing fractional states such as their elementary fractionally charged quasiparticles which often satisfy non-abelian statistics. I will provide a few applications of this approach, including the possibility to have fractional topological states in quasi-one dimensional systems. |