Volume 4, issue 1 (2004)

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

Volume 22
Issue 8, 3533–4008
Issue 7, 3059–3532
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Noncommutative knot theory

Tim D Cochran

Algebraic & Geometric Topology 4 (2004) 347–398
Bibliography
1 M F Atiyah, Elliptic operators, discrete groups and von Neumann algebras, from: "Colloque “Analyse et Topologie” en l'Honneur de Henri Cartan (Orsay, 1974)", Soc. Math. France (1976) MR0420729
2 M Boileau, S Wang, Non-zero degree maps and surface bundles over $S^1$, J. Differential Geom. 43 (1996) 789 MR1412685
3 K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1982) MR672956
4 J C Cha, Fibred knots and twisted Alexander invariants, Trans. Amer. Math. Soc. 355 (2003) 4187 MR1990582
5 T D Cochran, K E Orr, Homology boundary links and Blanchfield forms: concordance classification and new tangle-theoretic constructions, Topology 33 (1994) 397 MR1286923
6 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
7 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
8 T D Cochran, P Teichner, Knot concordance and von Neumann $\rho$–invariants, Duke Math. J. 137 (2007) 337 MR2309149
9 P M Cohn, Skew fields, Encyclopedia of Mathematics and its Applications 57, Cambridge University Press (1995) MR1349108
10 P M Cohn, Free rings and their relations, London Mathematical Society Monographs 19, Academic Press (1985) MR800091
11 J Cheeger, M Gromov, Bounds on the von Neumann dimension of $L^2$–cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
12 J Conant, P Teichner, Grope cobordism of classical knots, Topology 43 (2004) 119 MR2030589
13 J Dodziuk, P Linnell, V Mathai, T Schick, S Yates, Approximating $L^2$–invariants and the Atiyah conjecture, Comm. Pure Appl. Math. 56 (2003) 839 MR1990479
14 J Duval, Forme de Blanchfield et cobordisme d'entrelacs bords, Comment. Math. Helv. 61 (1986) 617 MR870709
15 S Garoufalidis, L Rozansky, The loop expansion of the Kontsevich integral, the null-move and $S$–equivalence, Topology 43 (2004) 1183 MR2080000
16 S Garoufalidis, J Levine, Homology surgery and invariants of 3–manifolds, Geom. Topol. 5 (2001) 551 MR1833753
17 C M Gordon, Some aspects of classical knot theory, from: "Knot theory (Proc. Sem., Plans-sur–Bex, 1977)", Lecture Notes in Math. 685, Springer (1978) 1 MR521730
18 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
19 S L Harvey, Higher-order polynomial invariants of 3–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
20 J Harer, How to construct all fibered knots and links, Topology 21 (1982) 263 MR649758
21 J Hempel, Intersection calculus on surfaces with applications to 3–manifolds, Mem. Amer. Math. Soc. 43 (1983) MR699242
22 G Higman, The units of group-rings, Proc. London Math. Soc. $(2)$ 46 (1940) 231 MR0002137
23 J A Hillman, Alexander ideals of links, Lecture Notes in Mathematics 895, Springer (1981) MR653808
24 N Higson, G Kasparov, preprint (1998)
25 P J Hilton, U Stammbach, A course in homological algebra, Graduate Texts in Mathematics 4, Springer (1971) MR0346025
26 J Howie, H R Schneebeli, Homological and topological properties of locally indicable groups, Manuscripta Math. 44 (1983) 71 MR709846
27 N Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys I, American Mathematical Society (1943) MR0008601
28 A Kawauchi, Almost identical imitations of $(3,1)$–dimensional manifold pairs, Osaka J. Math. 26 (1989) 743 MR1040422
29 R Kirby, A calculus for framed links in $S^{3}$, Invent. Math. 45 (1978) 35 MR0467753
30 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
31 P B Kronheimer, Embedded surfaces and gauge theory in three and four dimensions, from: "Surveys in differential geometry, Vol III (Cambridge, MA, 1996)", Int. Press, Boston (1998) 243 MR1677890
32 P B Kronheimer, Minimal genus in $S^1{\times}M^3$, Invent. Math. 135 (1999) 45 MR1664695
33 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
34 J Levine, Knot modules I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
35 J Lewin, A note on zero divisors in group-rings, Proc. Amer. Math. Soc. 31 (1972) 357 MR0292957
36 V Mathai, Spectral flow, eta invariants, and von Neumann algebras, J. Funct. Anal. 109 (1992) 442 MR1186326
37 J R Munkres, Elements of algebraic topology, Addison-Wesley Publishing Company (1984) MR755006
38 J R Munkres, Topology: a first course, Prentice-Hall (1975) MR0464128
39 D S Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons] (1977) MR470211
40 S Naik, T Stanford, A move on diagrams that generates $S$–equivalence of knots, J. Knot Theory Ramifications 12 (2003) 717 MR1999640
41 A Ranicki, Exact sequences in the algebraic theory of surgery, Mathematical Notes 26, Princeton University Press (1981) MR620795
42 S Roushon, Topology of 3–manifolds and a class of groups arXiv:math.GT/0209121
43 J R Stallings, Constructions of fibred knots and links, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 55 MR520522
44 J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR0175956
45 B Stenström, Rings of quotients, Grundlehren der Mathematischen Wissenschaften 217, Springer (1975) MR0389953
46 A Stoimenow, Vassiliev invariants on fibered and mutually obverse knots, J. Knot Theory Ramifications 8 (1999) 511 MR1697387
47 R Strebel, Homological methods applied to the derived series of groups, Comment. Math. Helv. 49 (1974) 302 MR0354896
48 G W Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics 61, Springer (1978) MR516508
49 C T C Wall, Surgery on compact manifolds, London Mathematical Society Monographs 1, Academic Press (1970) MR0431216