Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases

Understand

We review the dimensional reduction procedure in the group cohomology classification of bosonic SPT phases with finite abelian unitary symmetry group.

• We then extend this to include general reductions of arbitrary dimensions and also extend the procedure to fermionic SPT phases described by the Gu-Wen super-cohomology model.
• We then show that we can define topological invariants as partition functions on certain closed orientable/spin manifolds equipped with a flat connection.
• The invariants are able to distinguish all phases described within the respective models.