% Publication metadata reconciled 17 October 2026. Existing keys and arXiv
% versions are retained. Preprint-specific source locators are not silently
% reassigned to a journal edition by these bibliography-only changes.
\begin{thebibliography}{99}

\bibitem{AganagicShakirov}
M. Aganagic and S. Shakirov,
\emph{Knot homology and refined Chern--Simons index},
Commun. Math. Phys. \textbf{333} (2015), no.~1, 187--228;
\href{https://doi.org/10.1007/s00220-014-2197-4}{\nolinkurl{doi:10.1007/s00220-014-2197-4}};
preprint \emph{Knot homology from refined Chern--Simons theory},
\href{https://arxiv.org/abs/1105.5117}{arXiv:1105.5117}.

\bibitem{AlagicLo}
G. Alagic and C. Lo,
\emph{Quantum invariants of 3-manifolds and NP vs. \#P},
Quantum Inf. Comput. \textbf{17} (2017), nos.~1--2, 125--146;
\href{https://doi.org/10.26421/QIC17.1-2-8}{\nolinkurl{doi:10.26421/QIC17.1-2-8}};
\href{https://arxiv.org/abs/1411.6049}{arXiv:1411.6049}.

\bibitem{ArthamonovShakirov}
S. Arthamonov and Sh. Shakirov,
\emph{Refined Chern--Simons theory in genus two},
J. Knot Theory Ramifications \textbf{29} (2020), no.~7, 2050044;
\href{https://doi.org/10.1142/S0218216520500443}{\nolinkurl{doi:10.1142/S0218216520500443}};
\href{https://arxiv.org/abs/1504.02620}{arXiv:1504.02620}.

\bibitem{BCK}
H. Baik, I. Choi, and D.~M. Kim,
\emph{On the surjectivity of the symplectic representation of the mapping
class group},
Topology Appl. \textbf{322} (2022), 108334;
\href{https://doi.org/10.1016/j.topol.2022.108334}{\nolinkurl{doi:10.1016/j.topol.2022.108334}};
\href{https://arxiv.org/abs/2008.10142}{arXiv:2008.10142}.

\bibitem{BakshiPrzytycki}
R.~P. Bakshi and J.~H. Przytycki,
\emph{Kauffman bracket skein module of the connected sum of handlebodies:
a counterexample},
Manuscripta Math. \textbf{167} (2022), nos.~3--4, 809--820;
\href{https://doi.org/10.1007/s00229-021-01288-5}{\nolinkurl{doi:10.1007/s00229-021-01288-5}};
\href{https://arxiv.org/abs/2005.07750}{arXiv:2005.07750}.

\bibitem{BHMV}
C. Blanchet, N. Habegger, G. Masbaum, and P. Vogel,
\emph{Topological quantum field theories derived from the Kauffman bracket},
Topology \textbf{34} (1995), no.~4, 883--927;
\href{https://doi.org/10.1016/0040-9383(94)00051-4}{\nolinkurl{doi:10.1016/0040-9383(94)00051-4}}.

\bibitem{BullockFrohmanKania}
D. Bullock, C. Frohman, and J. Kania-Bartoszy\'nska,
\emph{The Yang--Mills measure in the Kauffman bracket skein module},
Comment. Math. Helv. \textbf{78} (2003), no.~1, 1--17;
\href{https://doi.org/10.1007/s000140300000}{\nolinkurl{doi:10.1007/s000140300000}};
\href{https://arxiv.org/abs/math/0005218}{arXiv:math/0005218}.

\bibitem{YangMills}
D. Bullock, C. Frohman, and J. Kania-Bartoszy\'nska,
\emph{The Yang--Mills measure in the Kauffman bracket skein module},
Comment. Math. Helv. \textbf{78} (2003), no.~1, 1--17;
\href{https://doi.org/10.1007/s000140300000}{\nolinkurl{doi:10.1007/s000140300000}};
\href{https://arxiv.org/abs/math/0005218}{arXiv:math/0005218}.

\bibitem{CHM}
D. Cheptea, K. Habiro, and G. Massuyeau,
\emph{A functorial LMO invariant for Lagrangian cobordisms},
Geom. Topol. \textbf{12} (2008), no.~2, 1091--1170;
\href{https://doi.org/10.2140/gt.2008.12.1091}{\nolinkurl{doi:10.2140/gt.2008.12.1091}};
\href{https://arxiv.org/abs/math/0701277}{arXiv:math/0701277}.

\bibitem{MappingTori}
S. Chun, S. Gukov, S. Park, and N. Sopenko,
\emph{3d--3d correspondence for mapping tori},
J. High Energy Phys. \textbf{2020} (2020), no.~9, 152;
\href{https://doi.org/10.1007/JHEP09(2020)152}{\nolinkurl{doi:10.1007/JHEP09(2020)152}};
\href{https://arxiv.org/abs/1911.08456}{arXiv:1911.08456}.

\bibitem{CochranMelvin}
T.~D. Cochran and P. Melvin,
\emph{Quantum cyclotomic orders of 3-manifolds},
Topology \textbf{40} (2001), no.~1, 95--125;
\href{https://doi.org/10.1016/S0040-9383(99)00056-7}{\nolinkurl{doi:10.1016/S0040-9383(99)00056-7}};
\href{https://arxiv.org/abs/math/9809129}{arXiv:math/9809129}.

\bibitem{Costantino}
F. Costantino,
\emph{Integrality of Kauffman brackets of trivalent graphs},
Quantum Topol. \textbf{5} (2014), no.~2, 143--184;
\href{https://doi.org/10.4171/QT/49}{\nolinkurl{doi:10.4171/QT/49}};
\href{https://arxiv.org/abs/0908.0542}{arXiv:0908.0542}.

\bibitem{CostantinoLe}
F. Costantino and T.~T.~Q. L\^e,
\emph{Stated skein modules of 3-manifolds and TQFT},
J. Inst. Math. Jussieu \textbf{24} (2025), no.~3, 663--703;
\href{https://doi.org/10.1017/S1474748024000550}{\nolinkurl{doi:10.1017/S1474748024000550}};
\href{https://arxiv.org/abs/2206.10906}{arXiv:2206.10906}.

\bibitem{GaroufalidisLe}
S. Garoufalidis and T.~T.~Q. L\^e,
\emph{Is the Jones polynomial of a knot really a polynomial?},
J. Knot Theory Ramifications \textbf{15} (2006), no.~8, 983--1000;
\href{https://doi.org/10.1142/S0218216506004919}{\nolinkurl{doi:10.1142/S0218216506004919}};
\href{https://arxiv.org/abs/math/0601139}{arXiv:math/0601139}.

\bibitem{GaroufalidisLe2023}
S. Garoufalidis and T.~T.~Q. L\^e,
\emph{From 3-dimensional skein theory to functions near \(\mathbb Q\)},
Ann. Inst. Fourier (Grenoble) \textbf{76} (2026), no.~4, 1473--1493;
\href{https://doi.org/10.5802/aif.3740}{\nolinkurl{doi:10.5802/aif.3740}};
\href{https://arxiv.org/abs/2307.09135v2}{arXiv:2307.09135v2}.

\bibitem{GhigginiLisca}
P. Ghiggini and P. Lisca,
\emph{Open book decompositions versus prime factorizations of closed,
oriented 3-manifolds},
Geom. Topol. Monogr. \textbf{19} (2015), 145--155;
\href{https://doi.org/10.2140/gtm.2015.19.145}{\nolinkurl{doi:10.2140/gtm.2015.19.145}};
\href{https://arxiv.org/abs/1407.2148}{arXiv:1407.2148}.

\bibitem{GilmerMasbaumLattices}
P.~M. Gilmer and G. Masbaum,
\emph{Integral lattices in TQFT},
Ann. Sci. \'Ec. Norm. Sup\'er. (4) \textbf{40} (2007), no.~5, 815--844;
\href{https://doi.org/10.1016/j.ansens.2007.07.002}{\nolinkurl{doi:10.1016/j.ansens.2007.07.002}};
\href{https://arxiv.org/abs/math/0411029}{arXiv:math/0411029}.

\bibitem{GilmerMasbaum}
P.~M. Gilmer and G. Masbaum,
\emph{Integral topological quantum field theory for a one-holed torus},
Pacific J. Math. \textbf{252} (2011), no.~1, 93--112;
\href{https://doi.org/10.2140/pjm.2011.252.93}{\nolinkurl{doi:10.2140/pjm.2011.252.93}};
preprint \emph{Integral TQFT for a one-holed torus},
\href{https://arxiv.org/abs/0908.2796}{arXiv:0908.2796}.

\bibitem{GukovManolescu}
S. Gukov and C. Manolescu,
\emph{A two-variable series for knot complements},
Quantum Topol. \textbf{12} (2021), no.~1, 1--109;
\href{https://doi.org/10.4171/QT/145}{\nolinkurl{doi:10.4171/QT/145}};
\href{https://arxiv.org/abs/1904.06057v2}{arXiv:1904.06057v2}.

\bibitem{GPPV1701}
S. Gukov, D. Pei, P. Putrov, and C. Vafa,
\emph{BPS spectra and 3-manifold invariants},
J. Knot Theory Ramifications \textbf{29} (2020), no.~2, 2040003;
\href{https://doi.org/10.1142/S0218216520400039}{\nolinkurl{doi:10.1142/S0218216520400039}};
\href{https://arxiv.org/abs/1701.06567v2}{arXiv:1701.06567v2}.

\bibitem{GPPV1602}
S. Gukov, P. Putrov, and C. Vafa,
\emph{Fivebranes and 3-manifold homology},
J. High Energy Phys. \textbf{2017} (2017), no.~7, 071;
\href{https://doi.org/10.1007/JHEP07(2017)071}{\nolinkurl{doi:10.1007/JHEP07(2017)071}};
\href{https://arxiv.org/abs/1602.05302v1}{arXiv:1602.05302v1}.

\bibitem{Habiro}
K. Habiro,
\emph{A unified Witten--Reshetikhin--Turaev invariant for integral homology
spheres},
Invent. Math. \textbf{171} (2008), no.~1, 1--81;
\href{https://doi.org/10.1007/s00222-007-0071-0}{\nolinkurl{doi:10.1007/s00222-007-0071-0}};
\href{https://arxiv.org/abs/math/0605314}{arXiv:math/0605314}.

\bibitem{Hansen}
S.~K. Hansen,
\emph{Reshetikhin--Turaev invariants of Seifert 3-manifolds and a rational
surgery formula},
Algebr. Geom. Topol. \textbf{1} (2001), 627--686;
\href{https://doi.org/10.2140/agt.2001.1.627}{\nolinkurl{doi:10.2140/agt.2001.1.627}};
\href{https://arxiv.org/abs/math/0111057}{arXiv:math/0111057}.

\bibitem{Koda}
Y. Koda,
\emph{Automorphisms of the 3-sphere that preserve spatial graphs and
handlebody-knots},
Math. Proc. Cambridge Philos. Soc. \textbf{159} (2015), no.~1, 1--22;
\href{https://doi.org/10.1017/S0305004114000723}{\nolinkurl{doi:10.1017/S0305004114000723}};
\href{https://arxiv.org/abs/1106.4777}{arXiv:1106.4777}.

\bibitem{KorinmanMurakami}
J. Korinman and J. Murakami,
\emph{Relating quantum character varieties and skein modules},
preprint (2022), \href{https://arxiv.org/abs/2211.04252}{arXiv:2211.04252}.

\bibitem{KLO}
T. Kuriya, T.~T.~Q. L\^e, and T. Ohtsuki,
\emph{The perturbative invariants of rational homology 3-spheres can be
recovered from the LMO invariant},
J. Topol. \textbf{5} (2012), no.~2, 458--484;
\href{https://doi.org/10.1112/jtopol/jts010}{\nolinkurl{doi:10.1112/jtopol/jts010}};
\href{https://arxiv.org/abs/1005.3895}{arXiv:1005.3895}.

\bibitem{LawrenceZagier}
R. Lawrence and D. Zagier,
\emph{Modular forms and quantum invariants of 3-manifolds},
Asian J. Math. \textbf{3} (1999), no.~1, 93--108;
\href{https://doi.org/10.4310/AJM.1999.v3.n1.a5}{\nolinkurl{doi:10.4310/AJM.1999.v3.n1.a5}}.

\bibitem{LePerturbative}
T.~T.~Q. L\^e,
\emph{Quantum invariants of 3-manifolds: integrality, splitting, and
perturbative expansion},
Topology Appl. \textbf{127} (2003), nos.~1--2, 125--152;
\href{https://doi.org/10.1016/S0166-8641(02)00056-1}{\nolinkurl{doi:10.1016/S0166-8641(02)00056-1}};
\href{https://arxiv.org/abs/math/0004099}{arXiv:math/0004099}.

\bibitem{LovejoyOsburnStorzer}
J. Lovejoy, R. Osburn, and M. Storzer,
\emph{Bailey pairs, Eichler integrals and unified
Witten--Reshetikhin--Turaev invariants}, preprint (2026), \href{https://arxiv.org/abs/2605.15740}{arXiv:2605.15740}.

\bibitem{Marche}
J. March\'e,
\emph{Introduction to quantum representations of mapping class groups},
in \emph{Topology and Geometry: A Collection of Essays Dedicated to Vladimir G. Turaev} (A. Papadopoulos, ed.), IRMA Lect. Math. Theor. Phys. \textbf{33}, EMS Press, Berlin, 2021, pp.~109--130;
\href{https://doi.org/10.4171/IRMA/33-1/7}{\nolinkurl{doi:10.4171/IRMA/33-1/7}};
\href{https://arxiv.org/abs/1812.03888}{arXiv:1812.03888}.

\bibitem{MasbaumVogel}
G. Masbaum and P. Vogel,
\emph{3-valent graphs and the Kauffman bracket},
Pacific J. Math. \textbf{164} (1994), no.~2, 361--381;
\href{https://doi.org/10.2140/pjm.1994.164.361}{\nolinkurl{doi:10.2140/pjm.1994.164.361}}.

\bibitem{Murakami}
Y. Murakami,
\emph{Witten--Reshetikhin--Turaev invariants and homological blocks for
plumbed homology spheres},
Commun. Number Theory Phys. \textbf{18} (2024), no.~2, 371--403;
\href{https://doi.org/10.4310/CNTP.2024.v18.n2.a3}{\nolinkurl{doi:10.4310/CNTP.2024.v18.n2.a3}};
\href{https://arxiv.org/abs/2205.01282}{arXiv:2205.01282}.

\bibitem{Przytycki}
J.~H. Przytycki,
\emph{Fundamentals of Kauffman bracket skein modules},
Kobe J. Math. \textbf{16} (1999), no.~1, 45--66;
\href{https://doi.org/10.24546/E0003677}{archived version of record};
\href{https://arxiv.org/abs/math/9809113}{arXiv:math/9809113}.

\bibitem{IntegralRootFibresClosedFactorizations2026}
H.-Y. Sun,
\emph{Integral root fibers and closed factorizations: Pairing maps, Rees covariance, caps, and sewing}, unpublished manuscript (2026).

\end{thebibliography}