3 problems

Let a path of paths mean a map from $S^2$ to the space of gapped Hamiltonians, and consider the spatially varying Hamiltonian obtained by mapping the plane to $S^2$ so that the ori…

Let $F$ map invertible states and domain walls in $(d-1)$ dimensions to paths of $d$-dimensional Hamiltonians, and let $G$ map paths of $d$-dimensional Hamiltonians to invertible s…

Let $\mathcal{S}$ be a connected component of the space of two-dimensional gapped Hamiltonians realizing a fixed topological order. Let invertible states be identified under equiva…