Orbifold Construction for Topological Field Theories

Abstract

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 construction which for any given morphism $G\to H$ of finite groups assigns in a functorial way to a $G$-equivariant topological field theory an $H$-equivariant topological field theory, the pushforward theory. When $H$ is the trivial group, this yields an orbifold construction for $G$-equivariant topological field theories which unifies and generalizes several known algebraic notions of orbifoldization.

21 pages, accepted for publication in the Journal of Pure and Applied Algebra

References in corpus (3)

• Modular categories as representations of the 3-dimensional bordism 2-category
• On $G$--equivariant modular categories
• Nakayama categories and groupoid quantization