Algebraic & Geometric Topology Volume 9, issue 2 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Surgery formulae for finite type invariants of rational homology $3$–spheres

Christine Lescop

Algebraic & Geometric Topology 9 (2009) 979–1047

DOI: 10.2140/agt.2009.9.979

Bibliography

1	S Akbulut, J D McCarthy, Casson’s invariant for oriented homology 3–spheres. An exposition, 36, Princeton Univ. Press (1990) MR1030042
2	E Auclair, Surfaces et invariants de type fini en dimension 3, PhD thesis, Grenoble University (2006)
3	E Auclair, C Lescop, Clover calculus for homology 3-spheres via basic algebraic topology, Algebr. Geom. Topol. 5 (2005) 71 MR2135546
4	S Axelrod, I M Singer, Chern–Simons perturbation theory, from: "Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991)" (editors S Catto, A Rocha), World Sci. Publ. (1992) 3 MR1225107
5	S Axelrod, I M Singer, Chern–Simons perturbation theory. II, J. Differential Geom. 39 (1994) 173 MR1258919
6	D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
7	D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres. I. A highly non trivial flat connection on S³, Selecta Math. (N.S.) 8 (2002) 315 MR1931167
8	D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres. II. Invariance and universality, Selecta Math. (N.S.) 8 (2002) 341 MR1931168
9	D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres. III. Relation with the Le–Murakami–Ohtsuki invariant, Selecta Math. (N.S.) 10 (2004) 305 MR2099069
10	R Bott, A S Cattaneo, Integral invariants of 3–manifolds, J. Differential Geom. 48 (1998) 91 MR1622602
11	R Bott, A S Cattaneo, Integral invariants of 3-manifolds. II, J. Differential Geom. 53 (1999) 1 MR1776090
12	A S Cattaneo, Configuration space integrals and invariants for 3–manifolds and knots, from: "Low-dimensional topology (Funchal, 1998)" (editor H Nencka), Contemp. Math. 233, Amer. Math. Soc. (1999) 153 MR1701680
13	S Garoufalidis, On finite type 3–manifold invariants. I, J. Knot Theory Ramifications 5 (1996) 441 MR1406715
14	S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75 MR1812435
15	S Garoufalidis, N Habegger, The Alexander polynomial and finite type 3–manifold invariants, Math. Ann. 316 (2000) 485 MR1752781
16	S Garoufalidis, T Ohtsuki, On finite type 3–manifold invariants. V. Rational homology 3–spheres, from: "Geometry and physics (Aarhus, 1995)" (editors J E Andersen, J Dupont, H Pedersen, A Swann), Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 445 MR1423186
17	C M Gordon, Some aspects of classical knot theory, from: "Knot theory (Proc. Sem., Plans-sur-Bex, 1977)" (editor J C Hausmann), Lecture Notes in Math. 685, Springer (1978) 1 MR521730
18	L Guillou, A Marin, Notes sur l’invariant de Casson des sphères d’homologie de dimension trois, Enseign. Math. (2) 38 (1992) 233 MR1189008
19	K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
20	C Kearton, W B R Lickorish, Piecewise linear critical levels and collapsing, Trans. Amer. Math. Soc. 170 (1972) 415 MR0310899
21	M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)" (editors A Joseph, F Mignot, F Murat, B Prum, R Rentschler), Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
22	G Kuperberg, D P Thurston, Perturbative 3–manifold invariants by cut-and-paste topology arXiv:math.GT/9912167
23	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" (editors V M Buchstaber, S P Novikov), Amer. Math. Soc. Transl. Ser. 2 179, Amer. Math. Soc. (1997) 75 MR1437158
24	T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
25	C Lescop, On the Kontsevich–Kuperberg–Thurston construction of a configuration space invariant for rational homology 3–spheres arXiv:math.GT/0411088
26	C Lescop, Splitting formulae for the Kontsevich–Kuperberg–Thurston invariant of rational homology 3–spheres arXiv:math.GT/0411431
27	C Lescop, Global surgery formula for the Casson–Walker invariant, 140, Princeton Univ. Press (1996) MR1372947
28	C Lescop, About the uniqueness of the Kontsevich integral, J. Knot Theory Ramifications 11 (2002) 759 MR1918812
29	A Marin, Un nouvel invariant pour les sphères d’homologie de dimension trois (d’après Casson), from: "Séminaire Bourbaki, Vol. 1987/88, Exp. No. 693", Astérisque 161-162 (1988) 151 MR992207
30	S V Matveev, Generalized surgeries of three-dimensional manifolds and representations of homology spheres, Mat. Zametki 42 (1987) 268, 345 MR915115
31	J Milnor, Link groups, Ann. of Math. (2) 59 (1954) 177 MR0071020
32	H Murakami, Y Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989) 75 MR995383
33	T Ohtsuki, Finite type invariants of integral homology 3–spheres, J. Knot Theory Ramifications 5 (1996) 101 MR1373813
34	H Rademacher, E Grosswald, Dedekind sums, 16, Math. Assoc. Amer. (1972) MR0357299
35	K Walker, An extension of Casson’s invariant, 126, Princeton Univ. Press (1992) MR1154798
36	C T C Wall, Quadratic forms on finite groups, and related topics, Topology 2 (1963) 281 MR0156890