Theoretical analysis demonstrates higher-loop perturbative invariants in framed 3-manifolds, highlighting an extension of Chern-Simons theory to non-acyclic flat connections.
Key Points
To review the mathematical generalization of Witten-Axelrod-Singer perturbative Chern-Simons invariants beyond acyclic flat connections.
Reviewed higher-loop perturbative invariant constructions for framed 3-manifolds.
Integrated a defined Chern-Simons volume form over a smooth closed component of the moduli space of flat connections.
Extended the classical perturbative Chern-Simons invariant framework to accommodate non-acyclic flat connections.
Established a well-defined topological invariant for framed 3-manifolds using integration over non-trivial moduli space components.