Volume 11, issue 3 (2007)

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

Volume 23
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
On the 2–loop polynomial of knots

Tomotada Ohtsuki

Geometry & Topology 11 (2007) 1357–1475
Bibliography
1 D Bar-Natan, S Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent. Math. 125 (1996) 103 MR1389962
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, S Garoufalidis, L Rozansky, D P Thurston, The \AArhus integral of rational homology 3–spheres III: Relation with the Le–Murakami–Ohtsuki invariant, Selecta Math. $($N.S.$)$ 10 (2004) 305 MR2099069
5 D Bar-Natan, R Lawrence, A rational surgery formula for the LMO invariant, Israel J. Math. 140 (2004) 29 MR2054838
6 D Bar-Natan, T T Q Le, D P Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geom. Topol. 7 (2003) 1 MR1988280
7 J Conant, Gropes and the rational lift of the Kontsevich integral arXiv:math.GT/0404270
8 D Gabai, Genera of the arborescent links, Mem. Amer. Math. Soc. 59 (1986) MR823442
9 S Garoufalidis, Signatures of links and finite type invariants of cyclic branched covers, from: "Tel Aviv Topology Conference: Rothenberg Festschrift (1998)", Contemp. Math. 231, Amer. Math. Soc. (1999) 87 MR1705577
10 S Garoufalidis, A Kricker, Finite type invariants of cyclic branched covers, Topology 43 (2004) 1247 MR2081426
11 S Garoufalidis, A Kricker, A rational noncommutative invariant of boundary links, Geom. Topol. 8 (2004) 115 MR2033481
12 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
13 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, Geom. Topol. Publ., Coventry (2002) 55 MR2002603
14 K Habiro, T T Q Le, in preparation
15 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 103 MR766964
16 S Kinoshita, H Terasaka, On unions of knots, Osaka Math. J. 9 (1957) 131 MR0098386
17 S Kojima, M Yamasaki, Some new invariants of links, Invent. Math. 54 (1979) 213 MR553219
18 M Kontsevich, Vassiliev's knot invariants, from: "I. M. Gel'fand Seminar", Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137 MR1237836
19 A Kricker, A surgery formula for the 2-loop piece of the LMO invariant of a pair, from: "Invariants of knots and 3-manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4 (2002) 161 MR2002609
20 A Kricker, Branched cyclic covers and finite type invariants, J. Knot Theory Ramifications 12 (2003) 135 MR1967238
21 A Kricker, The lines of the Kontsevich integral and Rozansky's rationality conjecture arXiv:math.GT/0005284
22 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 Buchstaber, S Novikov), Amer. Math. Soc. Transl. Ser. 2 179, Amer. Math. Soc. (1997) 75 MR1437158
23 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
24 W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997) MR1472978
25 J Marché, Cablages et intégrale de Kontsevich rationnelle en bas degré, PhD thesis, Université Paris 7 (2004)
26 J Marché, Surgery on a single clasper and the 2–loop part of the Kontsevich integral arXiv:math.GT/0410272
27 J Marché, An equivariant Casson invariant of knots in homology spheres, preprint (2005)
28 D Mullins, The generalized Casson invariant for 2–fold branched covers of $S^3$ and the Jones polynomial, Topology 32 (1993) 419 MR1217078
29 H Murakami, Quantum $\mathrm{SU}(2)$–invariants dominate Casson's $\mathrm{SU}(2)$–invariant, Math. Proc. Cambridge Philos. Soc. 115 (1994) 253 MR1277059
30 H Murakami, Quantum $\mathrm{SO}(3)$–invariants dominate the $\mathrm{SU}(2)$–invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995) 237 MR1307078
31 J Murakami, T Ohtsuki, Topological quantum field theory for the universal quantum invariant, Comm. Math. Phys. 188 (1997) 501 MR1473309
32 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
33 T Ohtsuki, Quantum invariants, Series on Knots and Everything 29, World Scientific Publishing Co. (2002) MR1881401
34 T Ohtsuki, Invariants of knots and 3–dimensional manifolds, Sūgaku 55 (2003) 337 MR2021547
35 T Ohtsuki, A cabling formula for the 2–loop polynomial of knots, Publ. Res. Inst. Math. Sci. 40 (2004) 949 MR2074706
36 T Ohtsuki, Equivariant quantum invariants of the infinite cyclic covers of knot complements, preprint, RIMS 15-9 (2005)
37 P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 MR2023281
38 P Ozsváth, Z Szabó, Knot Floer homology, genus bounds, and mutation, Topology Appl. 141 (2004) 59 MR2058681
39 L Rozansky, A rational structure of generating functions for Vassiliev invariants
40 L Rozansky, A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial, from: "Invariants of Three-Manifolds (Calgary, 1999)", Topology Appl. 127 (2003) 47 MR1953320