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By using quantum Teichm\"uller theory, we construct a one parameter family of TQFT's on the categroid of admissible leveled shaped 3-manifolds.
K. Hikami, Generalized Volume Conjecture and the A-Polynomials – the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant , J. Geom. Phys. 57
1940
Earlier work this paper cites.
L. Hørmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis CLassics in Mathematics, pp. 284, Springer 1963
1963
Earlier work this paper cites.
M. Reed & B. Simon, Methods of modern mathematical physics I: Functional analysis , pp. 325, Academic Press, New York, 1970
1970
Earlier work this paper cites.
M. Reed & B. Simon, Methods of modern mathematical physics II: Fourier analysis, self-adjointness , pp. 361, Academic Press, New York 1970
1970
Earlier work this paper cites.
W.D. Neumann, D. Zagier, Volumes of hyperbolic three-manifolds , Topology 24
1985
Earlier work this paper cites.
R. C. Penner, The decorated Teichmüller space of punctured surfaces , Comm. Math. Phys. 113
1987
Earlier work this paper cites.
M. Atiyah, Topological quantum field theories , Inst. Hautes Études Sci. Publ. Math. No. 68
1988
Earlier work this paper cites.
G.B. Segal, The definition of conformal field theory , Differential geometrical methods in theoretical physics (Como, 1987), 165–171, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 250, Kluwer Acad. Publ., Dordrecht, 1988
1988
Earlier work this paper cites.
E. Witten, Topological quantum field theory , Comm. Math. Phys. 117
1988
Earlier work this paper cites.
N. Reshetikhin & V. Turaev, Ribbon graphs and their invariants derived fron quantum groups , Comm. Math. Phys. 127
1990
Earlier work this paper cites.
N. Reshetikhin & V. Turaev, Invariants of 3 3 -manifolds via link polynomials and quantum groups , Invent. Math. 103
1991
Earlier work this paper cites.
C. Blanchet, N. Habegger, G. Masbaum & P. Vogel, Three-manifold invariants derived from the Kauffman Bracket . Topology 31
1992
Earlier work this paper cites.
R.M. Kashaev, Quantum dilogarithm as a 6j-symbol , Modern Phys. Lett. A 9
1994
Earlier work this paper cites.
V. G. Turaev, Quantum invariants of knots and 3-manifolds , de Gruyter Studies in Mathematics, 18. Walter de Gruyter & Co., Berlin, 1994
1994
Earlier work this paper cites.
C. Blanchet, N. Habegger, G. Masbaum & P. Vogel, Topological Quantum Field Theories derived from the Kauffman bracket . Topology 34
1995
Cited alongside, same era.
L.D. Faddeev, Discrete Heisenberg-Weyl group and modular group , Letters in Mathematical Physics 34
1995
Cited alongside, same era.
R.M. Kashaev, The hyperbolic volume of knots from quantum dilogarithm , Lett. Math. Phys. 39
1997
Cited alongside, same era.
R.M. Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm , Lett. Math. Phys. 43
1998
Cited alongside, same era.
L.O. Chekhov, V.V. Fock, Quantum Teichmüller spaces , Theor. Math. Phys. 120
1999
Cited alongside, same era.
I. Rivin: Combinatorial optimization in geometry, Adv. in Appl. Math. 31
2003
Later among the works it cites.
G. Gasper, M. Rahman, Basic hypergeometric series . With a foreword by Richard Askey. Second edition. Encyclopedia of Mathematics and its Applications, 96. Cambridge University Press, Cambridge, 2004
2004
Later among the works it cites.
A.Yu. Volkov, Noncommutative hypergeometry , Comm. Math. Phys. 258
2005
Later among the works it cites.
J.E. Andersen, Asymptotic faithfulness of the quantum SU ( n ) \mathop{SU}\nolimits(n) representations of the mapping class groups . Annals of Mathematics, 163
2006
Later among the works it cites.
J.E Andersen & S.K. Hansen, Asymptotics of the quantum invariants of surgeries on the figure 8 knot , Journal of Knot theory and its Ramifications, 15
2006
Later among the works it cites.
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1999
Cited alongside, same era.
M. Lackenby, Word hyperbolic Dehn surgery , Invent. Math., 140
2000
Cited alongside, same era.
R.M. Kashaev, On the Spectrum of Dehn Twists in Quantum Teichmüller Theory , Physics and Combinatorics 2000: Proceedings of Nagoya 2000 International Workshop, Graduate School of Mathematics, Nagoya University 21-26 August, (2000), 63–81
2000
Cited alongside, same era.
M. Lackenby, Word hyperbolic Dehn surgery , Invent. Math. 140 (2000) 243–282
2000
Cited alongside, same era.
L.D. Faddeev, R.M. Kashaev, and A.Yu. Volkov, Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality , Commun. Math. Phys. 219
2001
Cited alongside, same era.
K. Hikami, Hyperbolicity of Partition Function and Quantum Gravity , Nucl.Phys. B 616
2001
Cited alongside, same era.
H. Murakami, J. Murakami, The colored Jones polynomials and the simplicial volume of a knot , Acta Mathematica 186(1) (2001), 85–104
2001
Cited alongside, same era.
S. Baseilhac, R. Benedetti, Quantum hyperbolic geometry . Algebr. Geom. Topol. 7
2007
Later among the works it cites.
V.V. Bazhanov, V.V. Mangazeev, and S.M. Sergeev, Faddeev–Volkov solution of the Yang–Baxter equation and discrete conformal symmetry , Nucl. Phys. B 784
2007
Later among the works it cites.
J. Teschner, From Liouville theory to the quantum geometry of Riemann surfaces . Prospects in mathematical physics, 231–246, Contemp. Math., 437, Amer. Math. Soc., Providence, RI, 2007
2007
Later among the works it cites.
J. Teschner, An analog of a modular functor from quantized Teichmüller theory . Handbook of Teichmüller theory. Vol. I, 685–760, IRMA Lect. Math. Theor. Phys., 11, Eur. Math. Soc., Zürich, 2007
2007
Later among the works it cites.
V.V. Bazhanov, V.V. Mangazeev, and S.M. Sergeev, Quantum geometry of 3-dimensional lattices , J. Stat. Mech. 0807
2008
Later among the works it cites.
T. Dimofte, S. Gukov, J. Lenells, D. Zagier, Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group , Commun. Num. Theor. Phys. 3
2009
Later among the works it cites.
R. Dijkgraaf, H. Fuji, M. Manabe, The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings , Nucl. Phys. B 849
2011
Closest in time.
R. C. Penner, Decorated Teichmüller Theory , The QGM Master Class Series, 1
2012
Closest in time.