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 …

Modular functors, ie consistent systems of projective representations of mapping class
groups of surfaces, were constructed for nonsemisimple modular categories decades ago …

An equivariant topological field theory is defined on a cobordism category of manifolds with
principal fiber bundles for a fixed (finite) structure group. We provide a geometric …

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; …

Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum
Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional …

ON 3-DIMENSIONAL HOMOTOPY QUANTUM FIELD THEORY, I Page 1 International Journal of
Mathematics Vol. 23, No. 9 (2012) 1250094 (28 pages) c© World Scientific Publishing Company …

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 the G-centers of G-graded monoidal categories where G is an arbitrary group. We
prove that for any spherical G-fusion category C over an algebraically closed field such that …

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 …