• Hamiltonians, topology, and symmetry

  • Topology and symmetry
  • Zero-dimensional quantum systems
  • The concept of a topological invariant
  • Time-reversal symmetry
  • Sublattice symmetry
  • Particle-hole symmetry
  • Conclusion: Hamiltonians, topology, and symmetry

• Bulk-edge correspondence in the Kitaev chain

  • Kitaev chain and bulk-edge correspondence
  • Unpaired Majorana modes in one-dimensional systems
  • Topological phases from the bulk spectrum
  • Bulk topological invariant and the bulk-edge correspondence
  • Three approaches to analysing topological systems