Citation: Delaney, Colleen. A categorical perspective on symmetry, topological order, and quantum information. Diss. UC Santa Barbara, 2019.
Web: https://escholarship.org/uc/item/5z384290
Tags: Expository, Modular-tensor-categories, Property-F
This PhD thesis gives a review of modular tensor category theory, specifically insofar as it relates to topological order and quantum computation.
This thesis does not contain any substantially new results. There are some statements, conjectures, clarifications, and proofs which seem novel, but this is not the focus of the thesis. The focus is on the general theory as it has been developed over the last 25 years.
A special emphasis is put on the theory of symmetry enriched topological phases, with even more special emphasis put on the layer-exchange defect system. The precise way in which genons are equivalent to genus is explained.