Volume 8, issue 1 (2004)

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

Volume 29
Issue 2, 549–862
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
Editorial Board
Editorial Procedure
Subscriptions
 
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 rational noncommutative invariant of boundary links

Stavros Garoufalidis and Andrew Kricker

Geometry & Topology 8 (2004) 115–204
Bibliography
1 J E Andersen, J Mattes, N Reshetikhin, The Poisson structure on the moduli space of flat connections and chord diagrams, Topology 35 (1996) 1069 MR1404925
2 D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
3 D Bar-Natan, S Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent. Math. 125 (1996) 103 MR1389962
4 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
5 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
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 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
9 A Brownstein, R Lee, Cohomology of the group of motions of $n$ strings in 3–space, from: "Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991)", Contemp. Math. 150, Amer. Math. Soc. (1993) 51 MR1234259
10 J Berstel, C Reutenauer, Rational series and their languages, EATCS Monographs on Theoretical Computer Science 12, Springer (1988) MR971022
11 S E Cappell, J L Shaneson, The codimension two placement problem and homology equivalent manifolds, Ann. of Math. $(2)$ 99 (1974) 277 MR0339216
12 S E Cappell, J L Shaneson, Link cobordism, Comment. Math. Helv. 55 (1980) 20 MR569244
13 P M Cohn, Free rings and their relations, London Mathematical Society Monographs 19, Academic Press (1985) MR800091
14 J Duval, Forme de Blanchfield et cobordisme d'entrelacs bords, Comment. Math. Helv. 61 (1986) 617 MR870709
15 M Farber, P Vogel, The Cohn localization of the free group ring, Math. Proc. Cambridge Philos. Soc. 111 (1992) 433 MR1151322
16 M Farber, Noncommutative rational functions and boundary links, Math. Ann. 293 (1992) 543 MR1170526
17 M Farber, A Ranicki, The Morse–Novikov theory of circle-valued functions and noncommutative localization, Tr. Mat. Inst. Steklova 225 (1999) 381 MR1725953
18 R Fenn, C Rourke, On Kirby's calculus of links, Topology 18 (1979) 1 MR528232
19 S Garoufalidis, L Rozansky, The loop expansion of the Kontsevich integral, the null-move and $S$–equivalence, Topology 43 (2004) 1183 MR2080000
20 S Garoufalidis, J Levine, Homology surgery and invariants of 3–manifolds, Geom. Topol. 5 (2001) 551 MR1833753
21 S Garoufalidis, J Levine, Analytic invariants of boundary links, J. Knot Theory Ramifications 11 (2002) 283 MR1905685
22 S Garoufalidis, J Levine, Concordance and 1–loop clovers, Algebr. Geom. Topol. 1 (2001) 687 MR1875612
23 S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75 MR1812435
24 S Garoufalidis, to appear
25 S Garoufalidis, A Kricker, Finite type invariants of cyclic branched covers, Topology 43 (2004) 1247 MR2081426
26 S Garoufalidis, A Kricker, A surgery view of boundary links, Math. Ann. 327 (2003) 103 MR2005123
27 S Garoufalidis, P Teichner, On knots with trivial Alexander polynomial, J. Differential Geom. 67 (2004) 167 MR2153483
28 D L Goldsmith, The theory of motion groups, Michigan Math. J. 28 (1981) 3 MR600411
29 M A Gutiérrez, Boundary links and an unlinking theorem, Trans. Amer. Math. Soc. 171 (1972) 491 MR0310902
30 M Gutiérrez, S Krstić, Normal forms for basis-conjugating automorphisms of a free group, Internat. J. Algebra Comput. 8 (1998) 631 MR1682236
31 N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, Topology 39 (2000) 1253 MR1783857
32 M Kontsevich, Vassiliev's knot invariants, from: "I. M. Gel'fand Seminar", Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137 MR1237836
33 K H Ko, Seifert matrices and boundary link cobordisms, Trans. Amer. Math. Soc. 299 (1987) 657 MR869227
34 A Kricker, The lines of the Kontsevich integral and Rozansky's rationality conjecture arXiv:math/GT.0005284
35 A Kricker, Covering spaces over claspered knots arXiv:math.GT/9901029
36 J Levine, Knot modules I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
37 J P Levine, Link concordance and algebraic closure II, Invent. Math. 96 (1989) 571 MR996555
38 T T Q Le, J Murakami, Parallel version of the universal Vassiliev–Kontsevich invariant, J. Pure Appl. Algebra 121 (1997) 271 MR1477611
39 T T Q Le, H Murakami, J Murakami, T Ohtsuki, A three-manifold invariant via the Kontsevich integral, Osaka J. Math. 36 (1999) 365 MR1736483
40 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
41 J McCool, On basis-conjugating automorphisms of free groups, Canad. J. Math. 38 (1986) 1525 MR873421
42 B Patureau-Mirand, Caractères sur l'algèbre de diagrammes trivalents $\Lambda$, Geom. Topol. 6 (2002) 563 MR1941724
43 L Rozansky, Higher order terms in the Melvin–Morton expansion of the colored Jones polynomial, Comm. Math. Phys. 183 (1997) 291 MR1461960
44 L Rozansky, A contribution of a $U(1)$–reducible connection to quantum invariants of links I: R-matrix and Bureau representation arXiv:math.QA/9806004
45 L Rozansky, A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial, from: "Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three–Manifolds” (Calgary, AB, 1999)" (2003) 47 MR1953320
46 L Rozansky, A universal U(1)-RCC invariant of links and rationality conjecture arXiv:math.GT/0201139
47 J Roberts, Kirby calculus in manifolds with boundary, Turkish J. Math. 21 (1997) 111 MR1456165
48 N Smythe, Boundary links, from: "Topology Seminar (Wisconsin 1965)", Princeton University Press (1966) 69
49 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 79, 190 MR964255
50 M Farber, P Vogel, The Cohn localization of the free group ring, Math. Proc. Cambridge Philos. Soc. 111 (1992) 433 MR1151322