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Some years ago, it was conjectured by the first author that the Chern-Simons perturbation theory of a 3-manifold at the trivial flat connection is a resurgent power series.
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by same author, On the quantum sl 2 \rm sl_{2} invariants of knots and integral homology spheres , Invariants of knots and 3-manifolds (Kyoto, 2001), Geom. Topol. Monogr., vol. 4, Geom. Topol. Publ., Coventry, 2002, pp. 55–68 (electronic)
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Stavros Garoufalidis and Andrew Kricker, A rational noncommutative invariant of boundary links , Geom. Topol. 8
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by same author, Large color R R -matrix for knot complements and strange identities , 2004.02087
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Stavros Garoufalidis and Thang T. Q. Lê, The colored Jones function is q q -holonomic , Geom. Topol. 9
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Sergei Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A-polynomial , Comm. Math. Phys. 255
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Stavros Garoufalidis, Chern-Simons theory, analytic continuation and arithmetic , Acta Math. Vietnam. 33
2008
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Stavros Garoufalidis, Difference and differential equations for the colored Jones function , J. Knot Theory Ramifications 17
2008
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by same author, Gauge theories labelled by three-manifolds , Comm. Math. Phys. 325
2014
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Stavros Garoufalidis and Rinat Kashaev, Evaluation of state integrals at rational points , Commun. Number Theory Phys. 9
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David Sauzin, Nonlinear analysis with resurgent functions , Ann. Sci. Éc. Norm. Supér. (4) 48
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2008
Cited alongside, same era.
Tudor Dimofte, Sergei Gukov, Jonatan Lenells, and Don Zagier, Exact results for perturbative Chern-Simons theory with complex gauge group , Commun. Number Theory Phys. 3
2009
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by same author, On the origin and development of subfactors and quantum topology , Bull. Amer. Math. Soc. (N.S.) 46
2009
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Christoph Koutschan, HolonomicFunctions (user’s guide) , Tech. Report 10-01, RISC Report Series, Johannes Kepler University Linz, 2010
2010
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Ovidiu Costin and Stavros Garoufalidis, Resurgence of the Kontsevich-Zagier series , Ann. Inst. Fourier (Grenoble) 61
2011
Cited alongside, same era.
Stavros Garoufalidis and Thang T. Q. Lê, Asymptotics of the colored Jones function of a knot , Geom. Topol. 15
2011
Cited alongside, same era.
Hitoshi Murakami, An introduction to the volume conjecture , Interactions between hyperbolic geometry, quantum topology and number theory, Contemp. Math., vol. 541, Amer. Math. Soc., Providence, RI, January 2011, 1002.0126
2011
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2016
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Rinat Kashaev, Feng Luo, and Grigory Vartanov, A TQFT of Turaev-Viro type on shaped triangulations , Ann. Henri Poincaré 17
2016
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Rinat Kashaev and Marcos Marino, Operators from mirror curves and the quantum dilogarithm , Commun. Math. Phys. 346
2016
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by same author, From state integrals to q q -series , Math. Res. Lett. 24
2017
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Dongmin Gang and Yasuyuki Hatsuda, S-duality resurgence in SL ( 2 ) \rm SL(2) Chern-Simons theory , J. High Energy Phys. (2018), no. 7, 053, front matter+23
2018
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Sergei Gukov, Du Pei, Pavel Putrov, and Cumrun Vafa, BPS spectra and 3-manifold invariants , J. Knot Theory Ramifications 29
2020
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by same author, The resurgent structure of quantum knot invariants , Communications in Mathematical Physics 386
2021
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Stavros Garoufalidis and Rinat Kashaev, The descendant colored Jones polynomials , arXiv:2108.07553
2021
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Sergei Gukov and Ciprian Manolescu, A two-variable series for knot complements , Quantum Topol. 12
2021
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2021
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Stavros Garoufalidis and Don Zagier, Knots and their related q q -series , Preprint 2021
2021
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by same author, Knots, perturbative series and quantum modularity , Preprint 2021
2021
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Don Zagier, From 3-manifold invariants to number theory , Lecture course 2021
2021
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