Extended Homotopy Quantum Field Theories and their Orbifoldization

Understand

We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e.

• for $G$-equivariant topological field theories.
• More precisely, we use a bicategorical version of the parallel section functor to associate to an extended equivariant topological field theory an ordinary extended topological field theory.
• Thereby, we give a unification, geometric underpinning and vast generalization of algebraic concepts of orbifoldization.