Intro; Supervisor's Foreword; Acknowledgements; Contents; 1 Introduction; 1.1 Entanglement; 1.2 Topological Interactions; 1.3 Topological Response; 1.4 Outline; 1.5 Notations and Conventions for Topological Matter; References; 2 Anyons and Topological Order; 2.1 Bosons, Fermions and Abelian Anyons; 2.1.1 A Single Particle on An Annulus; 2.1.2 Indistinguishable Particles and the Braid Group; 2.1.3 Mediating Topological Interactions with a Gauge Boson; 2.2 Topological Order in Two Dimensions; 2.2.1 Torus Degeneracy; 2.3 Abelian Chern-Simons Theory; References

3 Response Theory and Symmetry Protected Topological Phases3.1 The Quantization of the Hall Conductance; 3.2 U(1) Response Theory; 3.2.1 Functional Bosonization; 3.3 The Wen-Zee Term and Chiral Superconductors; 3.3.1 Chiral Superconductors; References; 4 Topological Geometric Response and Topological Order of Super Conductors; 4.1 A Superconducting Bosonic Model; 4.2 Adding Fermions to Get Topological Order; 4.2.1 The Chiral p-Wave SC; 4.3 Non-Abelian Statistics in the Adiabatic Limit; 4.4 The Majorino Conundrum; References

A Conventions and Notation Concerning Differential Forms and U(1) ConnectionsA.1 Differential Forms; A.2 Normalization; Appendix B Definitions; Appendix C Vector Bundles and Chern Numbers in Quantum Mechanics; C.1 The Berry Connection; C.2 The Berry Field Strength; C.3 Chern Numbers and Chern-Simons Invariants; Reference