Volume 14, issue 3 (2014)

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
Infection by string links and new structure in the knot concordance group

John R Burke

Algebraic & Geometric Topology 14 (2014) 1577–1626
Bibliography
1 A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology, Part 2" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 39 MR520521
2 A J Casson, C M Gordon, Cobordism of classical knots, from: "Á la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 181 MR900252
3 J C Cha, The structure of the rational concordance group of knots, Mem. Amer. Math. Soc. 885, Amer. Math. Soc. (2007) MR2343079
4 J C Cha, Topological minimal genus and $L^2$–signatures, Algebr. Geom. Topol. 8 (2008) 885 MR2443100
5 T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
6 T D Cochran, S Friedl, P Teichner, New constructions of slice links, Comment. Math. Helv. 84 (2009) 617 MR2507256
7 T D Cochran, S Harvey, Homology and derived series of groups, II: Dwyer's theorem, Geom. Topol. 12 (2008) 199 MR2377249
8 T D Cochran, S Harvey, C Leidy, Link concordance and generalized doubling operators, Algebr. Geom. Topol. 8 (2008) 1593 MR2443256
9 T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
10 T D Cochran, S Harvey, C Leidy, Primary decomposition and the fractal nature of knot concordance, Math. Ann. 351 (2011) 443 MR2836668
11 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. 157 (2003) 433 MR1973052
12 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
13 T D Cochran, P Teichner, Knot concordance and von Neumann $\rho$–invariants, Duke Math. J. 137 (2007) 337 MR2309149
14 R H Fox, J W Milnor, Singularities of $2$–spheres in $4$–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
15 J A Hillman, Alexander ideals of links, Lecture Notes in Mathematics 895, Springer (1981) MR653808
16 B J Jiang, A simple proof that the concordance group of algebraically slice knots is infinitely generated, Proc. Amer. Math. Soc. 83 (1981) 189 MR620010
17 M A Kervaire, J W Milnor, On $2$–spheres in $4$–manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961) 1651 MR0133134
18 S G Kim, Polynomial splittings of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 59 MR2127228
19 S G Kim, T Kim, Polynomial splittings of metabelian von Neumann rho-invariants of knots, Proc. Amer. Math. Soc. 136 (2008) 4079 MR2425750
20 C Leidy, Higher-order linking forms, PhD thesis, Rice University (2004) arXiv:1204.5167v1
21 C Leidy, Higher-order linking forms for knots, Comment. Math. Helv. 81 (2006) 755 MR2271220
22 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
23 J Levine, Knot modules, I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
24 J Levine, Signature invariants of homology bordism with applications to links, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 395 MR1177436
25 D S Passman, The algebraic structure of group rings, Robert E Krieger Publishing Co. (1985) MR798076
26 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1990) MR1277811
27 N W Stoltzfus, Unraveling the integral knot concordance group, Mem. Amer. Math. Soc. 192, Amer. Math. Soc. (1977) MR0467764