Volume 7, issue 1 (2003)

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ISSN (electronic): 1364-0380
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Two applications of elementary knot theory to Lie algebras and Vassiliev invariants

Dror Bar-Natan, Thang T Q Le and Dylan P Thurston

Geometry & Topology 7 (2003) 1–31
Bibliography
1 A Alekseev, E Meinrenken, The non-commutative Weil algebra, Invent. Math. 139 (2000) 135 MR1728878
2 M Andler, A Dvorsky, S Sahi, Kontsevich quantization and invariant distributions on Lie groups, Ann. Sci. École Norm. Sup. $(4)$ 35 (2002) 371 MR1914002
3 D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
4 D Bar-Natan, Non-associative tangles, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 139 MR1470726
5 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, Wheels, wheeling, and the Kontsevich integral of the unknot, Israel J. Math. 119 (2000) 217 MR1802655
6 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The \AArhus integral of rational homology 3–spheres II: Invariance and universality, Selecta Math. $($N.S.$)$ 8 (2002) 341 MR1931168
7 D Bar-Natan, R Lawrence, A rational surgery formula for the LMO invariant, Israel J. Math. 140 (2004) 29 MR2054838
8 S V Chmutov, A N Varchenko, Remarks on the Vassiliev knot invariants coming from $\mathrm{ sl}_2$, Topology 36 (1997) 153 MR1410469
9 D Bar-Natan, Vassiliev and quantum invariants of braids, from: "The interface of knots and physics (San Francisco, CA, 1995)", Proc. Sympos. Appl. Math. 51, Amer. Math. Soc. (1996) 129 MR1372767
10 J Dixmier, Enveloping algebras, Graduate Studies in Mathematics 11, American Mathematical Society (1996) MR1393197
11 M Duflo, Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. École Norm. Sup. $(4)$ 10 (1977) 265 MR0444841
12 R Godement, Introduction à la théorie des groupes de Lie, Springer (2004) MR2047118
13 V Hinich, A Vaintrob, Cyclic operads and algebra of chord diagrams, Selecta Math. $($N.S.$)$ 8 (2002) 237 MR1913297
14 N Hitchin, J Sawon, Curvature and characteristic numbers of hyper–Kähler manifolds, Duke Math. J. 106 (2001) 599 MR1813238
15 M Kontsevich, Vassiliev's knot invariants, from: "I. M. Gel'fand Seminar", Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137 MR1237836
16 M Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003) 157 MR2062626
17 A Kricker, B Spence, I Aitchison, Cabling the Vassiliev invariants, J. Knot Theory Ramifications 6 (1997) 327 MR1457192
18 T Q T Le, J Murakami, Representation of the category of tangles by Kontsevich's iterated integral, Comm. Math. Phys. 168 (1995) 535 MR1328252
19 T Q T Le, J Murakami, The universal Vassiliev–Kontsevich invariant for framed oriented links, Compositio Math. 102 (1996) 41 MR1394520
20 T T Q Le, J Murakami, Parallel version of the universal Vassiliev–Kontsevich invariant, J. Pure Appl. Algebra 121 (1997) 271 MR1477611
21 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
22 J Lieberum, The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials, Doc. Math. 5 (2000) 275 MR1763301
23 T Mochizuki, On the morphism of Duflo–Kirillov type, J. Geom. Phys. 41 (2002) 73 MR1872382
24 J Murakami, T Ohtsuki, Topological quantum field theory for the universal quantum invariant, Comm. Math. Phys. 188 (1997) 501 MR1473309
25 D Thurston, Torus actions for the LMO invariant, in preparation
26 P Vogel, Algebraic structures on modules of diagrams, technical report, Université Paris VII (1995)