Witten’s asymptotic expansion conjecture (general 3-manifolds)

Establish the asymptotic expansion of the SU(2) Witten–Reshetikhin–Turaev invariant for every closed oriented 3-manifold Y as k→∞, namely prove that there exist Puiseux series W_S(τ) indexed by the Chern–Simons action values S∈CS(Y) such that (Y)∼∑_{S∈CS(Y)}e^{2πikS} W_S(k−1).

Background

The paper states Witten’s asymptotic expansion conjecture for SU(2) Chern–Simons theory and the associated WRT invariants, and proves it for Seifert fibered integral homology spheres. The conjecture asserts that the WRT invariant admits a Poincaré asymptotic expansion in terms of contributions from classical Chern–Simons action values.

While this work settles the conjecture for a broad class of manifolds (Seifert fibered homology spheres), the authors emphasize that the conjecture remains a central open problem in quantum topology for general closed oriented 3-manifolds.