Volume 4, issue 1 (2004)

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

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

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
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
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