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 …

Extending the work of the first author, we introduce a notion of semisimple topological field
theory in arbitrary even dimension and show that such field theories necessarily lead to …

Based on a detailed definition of extended homotopy quantum field theories we develop a
field-theoretic orbifold construction for these theories when the target space is the classifying …

Given a finite Z _2 Z 2-graded group ̂ GG^ with ungraded subgroup GG and a twisted
cocycle ̂ λ ∈ Z^ n (B ̂ G; U (1) _ π) λ^∈ Z n (BG^; U (1) π) which restricts to λ ∈ Z^ n (BG; …

We develop a general framework for the description of anomalies using extended functorial
field theories extending previous work by Freed and Monnier. In this framework, anomalies …

We study discrete symmetries of Dijkgraaf–Witten theories and their gauging in the
framework of (extended) functorial quantum field theory. Non-abelian group cohomology is …

We prove that the parallel transport of a flat n-1 n-1-gerbe on any given target space gives
rise to an n-dimensional extended homotopy quantum field theory. In case the target space …

We prove a decomposition formula for the dimensional reduction of an extended topological
field theory that arises as an orbifold of an equivariant topological field theory. Our …