Volume 10, issue 3 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Refined Kirby calculus for integral homology spheres

Kazuo Habiro

Geometry & Topology 10 (2006) 1285–1317
Bibliography
1 E H Brown Jr., Generalizations of the Kervaire invariant, Ann. of Math. $(2)$ 95 (1972) 368 MR0293642
2 R Fenn, C Rourke, On Kirby's calculus of links, Topology 18 (1979) 1 MR528232
3 S Garoufalidis, A Kricker, A surgery view of boundary links, Math. Ann. 327 (2003) 103 MR2005123
4 M Goussarov, Finite type invariants and $n$–equivalence of $3$–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
5 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
6 K Habiro, On the quantum $\mathrm{sl}_2$ invariants of knots and integral homology spheres, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4 (2002) 55 MR2002603
7 K Habiro, A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres, preprint (2006) arXiv:math.GT/0605314
8 K Habiro, T T Q Le, in preparation
9 J Hoste, A formula for Casson's invariant, Trans. Amer. Math. Soc. 297 (1986) 547 MR854084
10 R Kirby, A calculus for framed links in $S^3$, Invent. Math. 45 (1978) 35 MR0467753
11 R C Kirby, The topology of $4$–manifolds, Lecture Notes in Mathematics 1374, Springer (1989) MR1001966
12 R Kirby, P Melvin, The $3$–manifold invariants of Witten and Reshetikhin–Turaev for $\mathrm{sl}(2,\mathbb{C})$, Invent. Math. 105 (1991) 473 MR1117149
13 R Kirby, P Melvin, Local surgery formulas for quantum invariants and the Arf invariant, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7 (2004) 213 MR2172485
14 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
15 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of $3$–manifolds, Topology 37 (1998) 539 MR1604883
16 W B R Lickorish, A representation of orientable combinatorial $3$–manifolds, Ann. of Math. $(2)$ 76 (1962) 531 MR0151948
17 W Magnus, A Karrass, D Solitar, Combinatorial group theory, Dover Publications (1976) MR0422434
18 Y Matsumoto, An elementary proof of Rochlin's signature theorem and its extension by Guillou and Marin, from: "À la recherche de la topologie perdue", Progr. Math. 62, Birkhäuser (1986) 119 MR900248
19 J Nielsen, Die Isomorphismengruppe der freien Gruppen, Math. Ann. 91 (1924) 169 MR1512188
20 T Ohtsuki, Finite type invariants of integral homology $3$–spheres, J. Knot Theory Ramifications 5 (1996) 101 MR1373813
21 T Ohtsuki, Problems on invariants of knots and 3–manifolds, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4 (2002) 377 MR2065029
22 N Reshetikhin, V G Turaev, Invariants of $3$–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
23 D Rolfsen, Rational surgery calculus: extension of Kirby's theorem, Pacific J. Math. 110 (1984) 377 MR726496
24 C T C Wall, On the orthogonal groups of unimodular quadratic forms II, J. Reine Angew. Math. 213 (1963/1964) 122 MR0155798
25 A H Wallace, Modifications and cobounding manifolds, Canad. J. Math. 12 (1960) 503 MR0125588
26 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772