Adrian Chitan
Stratification of the Jeffrey-Weitsman half-density quantization of the Moduli Space of flat connections and Witten-Chern-Simons invariants
We present a novel reconstruction of the Jeffrey-Weitsman-Witten invariant through a stratified half-density quantization of the moduli space of flat connections, providing a rigorous and extended definition applicable to closed oriented 3-manifolds. Unlike previous approaches that rely solely on smooth components, this framework incorporates the entirety of the moduli space by leveraging the smooth stratified structure of the Lagrangian leaf. By defining a global volume form and a covariant constant half-density on the tangent spaces of the smooth strata, we naturally employ a reduction of the structure group at reducible connections. This construction is embellished with the level $k$ weighting conjectured by Freed and Gompf, where the $k^{(h^1 - h^0)/2}$ scaling factor arises as a consequence. We demonstrate that the resulting stratified BKS pairing exactly reproduces the topological invariant across all classes of flat connections, thereby extending and fortifying the invariant of Jeffrey-Weitsman and more closely approaching that of Witten's conjecture. In this talk we discuss this stratification and consider examples which showcase the refinement.
