Two types of topological phases have attracted a lot of
attention in condensed matter physics:
topological(SPT) phases and topologically ordered phases.
On the one hand, SPT phases are protected by given global symmetries while
there is no topological order in the bulk. On the other hand, topologically
ordered phases do not require symmetry and feature topological ground state
degeneracy. In this talk, I present a
classification of phases with both topological orders and global symmetries,
equipped with local bosonic exactly solvable models. This classification, in
some sense, organizes previous pieces of understandings on SPT phases,
topological orders, symmetry fractionalizations, into a single framework.
Solution of the exactly solvable models and measurable consequences will be