The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of $q$-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear $q$-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte-Gaiotto-Gukov 3D-index, and thus is given by a counting of BPS states. We illustrate our conjectures explicitly by matching theoretically and numerically computed integers for the cases of the $4_1$ and the $5_2$ knots.
Illuminating new and known relations between knot invariants
California Institute of Technology（加州理工学院）；Brigham Young University（杨百翰大学）；University of the Witwatersrand（威特沃特斯兰德大学）；University of British Columbia（不列颠哥伦比亚大学）
Resurgence of Chern-Simons theory at the trivial flat connection
International Center for Mathematics, Department of Mathematics Southern University of Science and Technology（南方科技大学数学系国际数学中心）；Université de Genève（日内瓦大学）；Shing-Tung Yau Center and School of Physics Southeast University（东南大学物理学院杨振宁中心）；Max Planck Institute for Mathematics（马克斯·普朗克数学研究所）
Algebraic structures of Vassiliev invariants for knot families
Institute for Theoretical and Experimental Physics（理论与实验物理研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Information Transmission Problems（信息传输问题研究所）；NRC ”Kurchatov Institute”（库尔恰托夫国家研究中心）
