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A functor-valued invariant of tangles

Mikhail Khovanov

Algebraic & Geometric Topology 2 (2002) 665–741
1 L Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory Ramifications 5 (1996) 569 MR1414088
2 S Ariki, On the decomposition numbers of the Hecke algebra of $G(m,1,n)$, J. Math. Kyoto Univ. 36 (1996) 789 MR1443748
3 V I Arnol’d, S M Guseĭn-Zade, A N Varchenko, Singularities of differentiable maps Vol I, Monographs in Mathematics 82, Birkhäuser (1985) MR777682
4 M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. (1988) MR1001453
5 J C Baez, J Dolan, Higher-dimensional algebra and topological quantum field theory, J. Math. Phys. 36 (1995) 6073 MR1355899
6 B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, American Mathematical Society (2001) MR1797619
7 A J Berkson, The $u$–algebra of a restricted Lie algebra is Frobenius, Proc. Amer. Math. Soc. 15 (1964) 14 MR0158910
8 J Bernstein, I Frenkel, M Khovanov, A categorification of the Temperley–Lieb algebra and Schur quotients of $U(\mathfrak{sl}_2)$ via projective and Zuckerman functors, Selecta Math. $($N.S.$)$ 5 (1999) 199 MR1714141
9 J N Bernstein, S I Gel’fand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980) 245 MR581584
10 A Bondal, D Orlov, Semiorthogonal decompositions for algebraic varieties, arXiv:alg-geom/9506012
11 P J Braam, S K Donaldson, Floer's work on instanton homology, knots and surgery, from: "The Floer memorial volume", Progr. Math. 133, Birkhäuser (1995) 195 MR1362829
12 T Braden, Perverse sheaves on Grassmannians, Canad. J. Math. 54 (2002) 493 MR1900761
13 T Braden, M Khovanov, in preparation,
14 T Bridgeland, Equivalences of triangulated categories and Fourier–Mukai transforms, Bull. London Math. Soc. 31 (1999) 25 MR1651025
15 J S Carter, D E Flath, M Saito, The classical and quantum 6$j$–symbols, Mathematical Notes 43, Princeton University Press (1995) MR1366832
16 J S Carter, L H Kauffman, M Saito, Diagrammatics, singularities, and their algebraic interpretations, Mat. Contemp. 13 (1997) 21 MR1630632
17 R W Carter, Representation theory of the 0–Hecke algebra, J. Algebra 104 (1986) 89 MR865891
18 L Crane, I B Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35 (1994) 5136 MR1295461
19 R Dijkgraaf, E Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393 MR1048699
20 H Strade, R Farnsteiner, Modular Lie algebras and their representations, Monographs and Textbooks in Pure and Applied Mathematics 116, Marcel Dekker (1988) MR929682
21 P Di Francesco, O Golinelli, E Guitter, Meanders and the Temperley–Lieb algebra, Comm. Math. Phys. 186 (1997) 1 MR1462755
22 I B Frenkel, N Jing, W Wang, Vertex representations via finite groups and the McKay correspondence, Internat. Math. Res. Notices (2000) 195 MR1747618
23 I B Frenkel, M G Khovanov, Canonical bases in tensor products and graphical calculus for $U_q(\mathfrak{sl}_2)$, Duke Math. J. 87 (1997) 409 MR1446615
24 K Fukaya, Floer homology for 3–manifolds with boundary, from: "Topology, geometry and field theory", World Sci. Publ., River Edge, NJ (1994) 1 MR1312167
25 K Fukaya, P Seidel, Floer homology, $A_\infty$–categories and topological field theory, from: "Geometry and physics (Aarhus, 1995)", Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 9 MR1423154
26 D Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series 119, Cambridge University Press (1988) MR935124
27 R S Huerfano, M Khovanov, A category for the adjoint representation, J. Algebra 246 (2001) 514 MR1872113
28 B Iversen, Cohomology of sheaves, Universitext, Springer (1986) MR842190
29 J C Jantzen, Representations of algebraic groups, Pure and Applied Mathematics 131, Academic Press (1987) MR899071
30 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 103 MR766964
31 L Kadison, New examples of Frobenius extensions, University Lecture Series 14, American Mathematical Society (1999) MR1690111
32 M Kapranov, E Vasserot, Kleinian singularities, derived categories and Hall algebras, Math. Ann. 316 (2000) 565 MR1752785
33 M Kashiwara, P Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften 292, Springer (1990) MR1074006
34 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
35 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, Annals of Mathematics Studies 134, Princeton University Press (1994) MR1280463
36 M Khovanov, Nilcoxeter algebras categorify the Weyl algebra, Comm. Algebra 29 (2001) 5033 MR1856929
37 M Khovanov, Graphical calculus, canonical bases and Kazhdan–Lusztig theory, PhD thesis, Yale University (1997)
38 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
39 M Khovanov, P Seidel, Quivers, Floer cohomology, and braid group actions, J. Amer. Math. Soc. 15 (2002) 203 MR1862802
40 A N Kirillov, N Y Reshetikhin, Representations of the algebra ${U}_q(\mathrm{sl}(2)),q$–orthogonal polynomials and invariants of links, from: "Infinite-dimensional Lie algebras and groups (Luminy–Marseille, 1988)", Adv. Ser. Math. Phys. 7, World Sci. Publ., Teaneck, NJ (1989) 285 MR1026957
41 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)", Birkhäuser (1995) 120 MR1403918
42 G Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
43 T Y Lam, Lectures on modules and rings, Graduate Texts in Mathematics 189, Springer (1999) MR1653294
44 M Mackaay, Finite groups, spherical 2–categories, and 4–manifold invariants, Adv. Math. 153 (2000) 353 MR1770934
45 G Malle, A Mathas, Symmetric cyclotomic Hecke algebras, J. Algebra 205 (1998) 275 MR1631350
46 H Nakajima, Instantons on ALE spaces, quiver varieties, and Kac–Moody algebras, Duke Math. J. 76 (1994) 365 MR1302318
47 A Polishchuk, Gluing of perverse sheaves on the basic affine space, Selecta Math. $($N.S.$)$ 7 (2001) 83 MR1856554
48 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
49 J Rickard, Triangulated categories in the modular representation theory of finite groups, from: "Derived equivalences for group rings", Lecture Notes in Math. 1685, Springer (1998) 177 MR1649845
50 R Rouquier, Action du groupe de tresses sur la catégorie dériveé de la variété de drapeaux, preprint
51 R Rouquier, Travaux de recherches. Représentations et catégories dérivées, (1998)
52 R Rouquier, A Zimmermann, Picard groups for derived module categories, Proc. London Math. Soc. $(3)$ 87 (2003) 197 MR1978574
53 P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
54 M E Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, New York (1969) MR0252485
55 V G Turaev, Quantum invariants of knots and 3–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
56 W Wang, Algebraic structures behind Hilbert schemes and wreath products, from: "Recent developments in infinite-dimensional Lie algebras and conformal field theory (Charlottesville, VA, 2000)", Contemp. Math. 297, Amer. Math. Soc. (2002) 271 MR1919822
57 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772