We investigate a family of invertible phases of matter with higher-dimensional exotic
excitations in even spacetime dimensions, which includes and generalizes the Kitaev's …

We provide a mathematical proposal for the anomaly indicators of symmetries of (2+ 1)-d
fermionic topological orders, and work out the consequences of our proposal in several …

We discuss the codimension-1 defects of (2+ 1) D bosonic topological phases, where the
defects can support fermionic degrees of freedom. We refer to such defects as fermionic …

We review a recipe to produce a lattice construction of fermionic phases of matter in the
presence of time reversal symmetry by extending the fermionization and bosonization …