2025/10/12 by Andersen, Jørgen Ellegaard, Han, Li, Li, Yong +3 · 2 citations
#57R56 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2510.10678
Let X be a general Seifert fibered integral homology 3-sphere with r≥3 exceptional fibers. For every root of unity ζ\not=1, we show that the SU(2) WRT invariant of X evaluated at ζ is (up to an elementary factor) the non-tangential limit at ζ of the GPPV invariant of X, thereby generalizing a result from [Andersen-Mistegard 2022]. Based on this result, we apply the quantum modularity results developed in [Han-Li-Sauzin-Sun 2023] to the GPPV invariant of X to prove Witten's asymptotic expansion conjecture [Witten 1989] for the WRT invariant of X. We also prove that the GPPV invariant of X induces a higher depth strong quantum modular form. Moreover, when suitably normalized, the GPPV invariant provides an ``analytic incarnation'' of the Habiro invariant.