Geometry & Topology Volume 12, issue 2 (2008)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A functorial LMO invariant for Lagrangian cobordisms

Dorin Cheptea, Kazuo Habiro and Gwénaël Massuyeau

Geometry & Topology 12 (2008) 1091–1170

DOI: 10.2140/gt.2008.12.1091

Bibliography

1	D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
2	D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The \AArhus integral of rational homology 3-spheres. I. A highly non trivial flat connection on $S^3$, Selecta Math. $($N.S.$)$ 8 (2002) 315 MR1931167
3	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
4	D Bar-Natan, R Lawrence, A rational surgery formula for the LMO invariant, Israel J. Math. 140 (2004) 29 MR2054838
5	D Cheptea, T T Q Le, Three-cobordisms with their rational homology on the boundary, preprint (2005) to appear in J. Knot Theory Ramifications arXiv:math/0508220
6	D Cheptea, T T Q Le, A TQFT associated to the LMO invariant of three-dimensional manifolds, Comm. Math. Phys. 272 (2007) 601 MR2304469
7	L Crane, D Yetter, On algebraic structures implicit in topological quantum field theories, J. Knot Theory Ramifications 8 (1999) 125 MR1687553
8	S Garoufalidis, The mystery of the brane relation, J. Knot Theory Ramifications 11 (2002) 725 MR1918810
9	S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75 MR1812435
10	S Garoufalidis, J Levine, Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism, from: "Graphs and patterns in mathematics and theoretical physics", Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 173 MR2131016
11	M Goussarov, Finite type invariants and $n$–equivalence of $3$–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
12	M Goussarov, Variations of knotted graphs. The geometric technique of $n$–equivalence, Algebra i Analiz 12 (2000) 79 MR1793618
13	N Habegger, Milnor, Johnson and tree-level perturbative invariants, preprint (2000)
14	N Habegger, X S Lin, On link concordance and Milnor's $\overline {\mu}$ invariants, Bull. London Math. Soc. 30 (1998) 419 MR1620841
15	N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, Topology 39 (2000) 1253 MR1783857
16	K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
17	K Habiro, Bottom tangles and universal invariants, Algebr. Geom. Topol. 6 (2006) 1113 MR2253443
18	D M Jackson, I Moffatt, A Morales, On the group-like behavior of the Le–Murakami–Ohtsuki invariant, J. Knot Theory Ramifications 16 (2007) 699 MR2341311
19	T Kerler, Bridged links and tangle presentations of cobordism categories, Adv. Math. 141 (1999) 207 MR1671770
20	T Kerler, Towards an algebraic characterization of 3–dimensional cobordisms, from: "Diagrammatic morphisms and applications (San Francisco, CA, 2000)", Contemp. Math. 318, Amer. Math. Soc. (2003) 141 MR1973515
21	T T Q Le, An invariant of integral homology $3$–spheres which is universal for all finite type invariants, from: "Solitons, geometry, and topology: on the crossroad", Amer. Math. Soc. Transl. Ser. 2 179, Amer. Math. Soc. (1997) 75 MR1437158
22	T Q T Le, The LMO invariant, lecture notes from: “Ecole d’Eté de Mathématiques: Invariants de noeuds et de variétés de dimension trois”, Institut Fourier (1999)
23	T Q T Le, J Murakami, Representation of the category of tangles by Kontsevich's iterated integral, Comm. Math. Phys. 168 (1995) 535 MR1328252
24	T Q T Le, J Murakami, The universal Vassiliev–Kontsevich invariant for framed oriented links, Compositio Math. 102 (1996) 41 MR1394520
25	T T Q Le, J Murakami, Parallel version of the universal Vassiliev–Kontsevich invariant, J. Pure Appl. Algebra 121 (1997) 271 MR1477611
26	T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of $3$–manifolds, Topology 37 (1998) 539 MR1604883
27	C Lescop, Splitting formulae for the Kontsevich–Kuperberg–Thurston invariant of rational homology $3$–spheres, preprint (2004) arXiv:math/0411431
28	G Massuyeau, Finite-type invariants of 3–manifolds and the dimension subgroup problem, J. Lond. Math. Soc. $(2)$ 75 (2007) 791 MR2352736
29	S V Matveev, Generalized surgeries of three-dimensional manifolds and representations of homology spheres, Mat. Zametki 42 (1987) 268, 345 MR915115
30	J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. $(2)$ 81 (1965) 211 MR0174052
31	I Moffatt, The \AArhus integral and the $\mu$–invariants, J. Knot Theory Ramifications 15 (2006) 361 MR2217502
32	S Morita, On the structure of the Torelli group and the Casson invariant, Topology 30 (1991) 603 MR1133875
33	H Murakami, Y Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989) 75 MR995383
34	J Murakami, T Ohtsuki, Topological quantum field theory for the universal quantum invariant, Comm. Math. Phys. 188 (1997) 501 MR1473309
35	T Ohtsuki, Quantum invariants, Series on Knots and Everything 29, World Scientific Publishing Co. (2002) MR1881401
36	J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR0175956