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In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants.
K. F. Gauss, (Translation by J. C. Morehead), General Investigations of Curved Surfaces , Princeton University Library, 1902, available at http://books.google.com/books?id=a1wTJR3kHwUC&dq
1902
Earlier work this paper cites.
1906
Earlier work this paper cites.
1909
Earlier work this paper cites.
W. Franz, Über die Torsion einer Überdeckung , J. Reine Angew. Math. 173
1935
Earlier work this paper cites.
K. Reidemeister, Homotopieringe und Linsenrüme , Abh. Math. Sem. Univ. Hamburg 11
1935
Earlier work this paper cites.
S-S Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds , Ann. of Math. (2) 45
1944
Earlier work this paper cites.
R. P. Feynman, Space-time approach to non-relativistic quantum mechanics , Rev. Modern Physics 20
1948
Earlier work this paper cites.
J. M. Boardman, R. M. Vogt, Homotopy invariant algebraic structures on topological spaces , Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin, 1973
1973
Earlier work this paper cites.
S-S Chern, J. Simons, Characteristic forms and geometric invariants , Ann. of Math. (2) 99
1974
Earlier work this paper cites.
P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, Real homotopy theory of Kähler manifolds , Invent. Math. 29
1975
Earlier work this paper cites.
K. G. Wilson, The renormalization group: critical phenomena and the Kondo problem , Rev. Modern Phys. 47
1975
Earlier work this paper cites.
M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. III , Math. Proc. Cambridge Philos. Soc. 79
1976
Earlier work this paper cites.
M. W. Hirsch, Differential topology , Graduate Texts in Mathematics, vol. 33, Springer-Verlag, New York, 1994, Corrected reprint of the 1976 original
1976
Earlier work this paper cites.
G. ’t Hooft, Naturalness chiral symmetry and spontaneous chiral symmetry breaking , Recent Developments in Gauge Theories (G ’t Hooft et. al., ed.), Plenum Press, New York, 1980
1980
Earlier work this paper cites.
R. S. Hamilton, Three-manifolds with positive Ricci curvature , J. Differential Geom. 17
1982
Earlier work this paper cites.
J. Polchinski, Renormalization and effective Lagrangians , Nuclear Phys. B 231
1984
Earlier work this paper cites.
P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, A. Ocneanu, A new polynomial invariant of knots and links , Bull. Amer. Math. Soc. (N.S.) 12
1985
Earlier work this paper cites.
D. H. Friedan, Nonlinear models in 2 + ϵ 2+\epsilon dimensions , Annals Phys. 163
1985
Earlier work this paper cites.
V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras , Bull. Amer. Math. Soc. (N.S.) 12
1985
Earlier work this paper cites.
by same author, Determinants, torsion, and strings , Comm. Math. Phys. 107
1986
Earlier work this paper cites.
J. Glimm, A. Jaffe, Quantum physics , second ed., Springer-Verlag, New York, 1987, A functional integral point of view
1987
Earlier work this paper cites.
V. G. Kac, M. Wakimoto, Modular and conformal invariance constraints in representation theory of affine algebras , Adv. in Math. 70
1988
Earlier work this paper cites.
G. Moore, N. Seiberg, Polynomial equations for rational conformal field theories , Phys. Lett. B 212
1988
Earlier work this paper cites.
J. H. Przytycki, P. Traczyk, Invariants of links of Conway type , Kobe J. Math. 4
1988
Earlier work this paper cites.
E. Verlinde, Fusion rules and modular transformations in 2 2 D conformal field theory , Nuclear Phys. B 300
1988
Earlier work this paper cites.
by same author, 2 + 1 2+1 -dimensional gravity as an exactly soluble system , Nuclear Phys. B 311
1988
Cited alongside, same era.
by same author, Topological quantum field theory , Comm. Math. Phys. 117
1988
Cited alongside, same era.
by same author, Topological quantum field theories , Inst. Hautes Études Sci. Publ. Math. (1988), no. 68, 175–186 (1989)
1989
Cited alongside, same era.
George W. Mackey, Unitary group representations in physics, probability, and number theory , second ed., Advanced Book Classics, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, 1989
1989
Cited alongside, same era.
E. Witten, Quantum field theory and the Jones polynomial , Comm. Math. Phys. 121
1989
Cited alongside, same era.
L. Rozansky, A large k k asymptotics of Witten’s invariant of Seifert manifolds , Commun. Math. Phys. 171
1995
Later among the works it cites.
L. Abrams, Two-dimensional topological quantum field theories and Frobenius algebras , J. Knot Theory Ramifications 5
1996
Later among the works it cites.
R. Bott, Critical point theory in mathematics and in mathematical physics , Turkish J. Math. 21
1997
Later among the works it cites.
M. Karowski, R. Schrader, E. Vogt, Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations , Experiment. Math. 6
1997
Later among the works it cites.
L. Rozansky, E. Witten, Hyper-Kähler geometry and invariants of three-manifolds , Selecta Math. (N.S.) 3
1997
Later among the works it cites.
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1990
Cited alongside, same era.
R. Dijkgraaf , E. Witten, Topological gauge theories and group cohomology , Comm. Math. Phys. 129
1990
Cited alongside, same era.
S. K. Donaldson, Polynomial invariants for smooth four-manifolds , Topology 29
1990
Cited alongside, same era.
V. A. Vassiliev, Cohomology of knot spaces , Theory of singularities and its applications, Adv. Soviet Math., vol. 1, Amer. Math. Soc., Providence, RI, 1990, pp. 23–69
1990
Cited alongside, same era.
D. S. Freed, R. E. Gompf, Computer calculation of Witten’s 3 3 -manifold invariant , Comm. Math. Phys. 141
1991
Cited alongside, same era.
A. Joyal, R. Street, Tortile Yang-Baxter operators in tensor categories , J. Pure Appl. Algebra 71
1991
Cited alongside, same era.
N. Reshetikhin, V. G. Turaev, Invariants of 3 3 -manifolds via link polynomials and quantum groups , Invent. Math. 103
1991
Cited alongside, same era.
R. Gopakumar, C. Vafa, Topological gravity as large N N topological gauge theory , Adv. Theor. Math. Phys. 2
1998
Later among the works it cites.
P. Deligne, D. S. Freed, Classical field theory , Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 137–225
1999
Later among the works it cites.
B. Bakalov, A. Kirillov, Jr., Lectures on tensor categories and modular functors , University Lecture Series, vol. 21, American Mathematical Society, Providence, RI, 2001
2001
Later among the works it cites.
by same author, The Verlinde algebra is twisted equivariant K K -theory , Turkish J. Math. 25
2001
Later among the works it cites.
M. J. Hopkins, Algebraic topology and modular forms , Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002) (Beijing), Higher Ed. Press, 2002, arXiv:math/0212397
2002
Later among the works it cites.
A. Joyal, Quasi-categories and Kan complexes , J. Pure Appl. Algebra 175
2002
Later among the works it cites.
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, E. Zaslow, Mirror symmetry , Clay Mathematics Monographs, vol. 1, American Mathematical Society, Providence, RI, 2003, With a preface by Vafa
2003
Later among the works it cites.
C. Manolescu, Seiberg-Witten-Floer stable homotopy type of three-manifolds with b 1 = 0 b_{1}=0 , Geom. Topol. 7
2003
Later among the works it cites.
M. Müger, From subfactors to categories and topology II: The quantum double of tensor categories and subfactors , J. Pure Appl. Algebra 180
2003
Later among the works it cites.
J. Roberts, Rozansky-Witten theory , Topology and geometry of manifolds (Athens, GA, 2001), Proc. Sympos. Pure Math., vol. 71, Amer. Math. Soc., Providence, RI, 2003, pp. 1–17, arXiv:math/0112209
2003
Later among the works it cites.
A. Beilinson, V. Drinfeld, Chiral algebras , American Mathematical Society Colloquium Publications, vol. 51, American Mathematical Society, Providence, RI, 2004
2004
Later among the works it cites.
E. Frenkel, D. Ben-Zvi, Vertex algebras and algebraic curves , second ed., Mathematical Surveys and Monographs, vol. 88, American Mathematical Society, Providence, RI, 2004
2004
Later among the works it cites.
J. Kock, Frobenius algebras and 2D topological quantum field theories , London Mathematical Society Student Texts, vol. 59, Cambridge University Press, Cambridge, 2004
2004
Later among the works it cites.
J. Mickelsson, Gerbes, (twisted) K K -theory, and the supersymmetric WZW model , Infinite dimensional groups and manifolds, IRMA Lect. Math. Theor. Phys., vol. 5, de Gruyter, Berlin, 2004, pp. 93–107, arXiv:hep-th/0206139
2004
Later among the works it cites.
by same author, The definition of conformal field theory , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 421–577
2004
Later among the works it cites.
S. Stolz, P. Teichner, What is an elliptic object? , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 247–343
2004
Later among the works it cites.
E. Friedlander, M. Walker, Semi-topological K K -theory , Handbook of K K -theory, Springer-Verlag, Berlin, 2005, pp. 877–924
2005
Later among the works it cites.
K. Costello, Topological conformal field theories and Calabi-Yau categories , Adv. Math. 210
2007
Later among the works it cites.
A. Kapustin, E. Witten, Electric-magnetic duality and the geometric Langlands program , Commun. Number Theory Phys. 1
2007
Later among the works it cites.