Volume 12, issue 2 (2012)

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

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
A second order algebraic knot concordance group

Mark Powell

Algebraic & Geometric Topology 12 (2012) 685–751
Bibliography
1 R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. 65 (1957) 340 MR0085512
2 S E Cappell, J L Shaneson, The codimension two placement problem and homology equivalent manifolds, Ann. of Math. 99 (1974) 277 MR0339216
3 A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 181 MR900252
4 J C Cha, K E Orr, L(2)–signatures, homology localization and amenable groups, Comm. Pure and Appl. Math. 65 (2012) 790
5 T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
6 T D Cochran, S Harvey, C Leidy, Derivatives of knots and second-order signatures, Algebr. Geom. Topol. 10 (2010) 739 MR2606799
7 T D Cochran, S Harvey, C Leidy, Primary decomposition and the fractal nature of knot concordance, Math. Ann. 351 (2011) 443 MR2836668
8 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L2–signatures, Ann. of Math. 157 (2003) 433 MR1973052
9 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
10 T D Cochran, P Teichner, Knot concordance and von Neumann ρ–invariants, Duke Math. J. 137 (2007) 337 MR2309149
11 P M Gilmer, Slice knots in S3, Quart. J. Math. Oxford Ser. 34 (1983) 305 MR711523
12 N Higson, G Kasparov, Operator K–theory for groups which act properly and isometrically on Hilbert space, Electron. Res. Announc. Amer. Math. Soc. 3 (1997) 131 MR1487204
13 C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. 10 (1975) 406 MR0385873
14 T Kim, Filtration of the classical knot concordance group and Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 137 (2004) 293 MR2092061
15 R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977) MR0645390
16 C F Letsche, An obstruction to slicing knots using the eta invariant, Math. Proc. Cambridge Philos. Soc. 128 (2000) 301 MR1735303
17 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
18 J Levine, Knot modules. I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
19 M Powell, A second order algebraic knot concordance group, PhD thesis, Edinburgh University (2011) arXiv:1109.0761v1
20 A Ranicki, The algebraic theory of surgery. I Foundations, II Applications to topology, Proc. London Math. Soc. 40 (1980) 87, 193 MR560997
21 A Ranicki, Exact sequences in the algebraic theory of surgery, 26, Princeton Univ. Press (1981) MR620795
22 A Ranicki, Algebraic and geometric surgery, , Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (2002) MR2061749
23 A Ranicki, Blanchfield and Seifert algebra in high-dimensional knot theory, Mosc. Math. J. 3 (2003) 1333 MR2058802
24 B Stenström, Rings of quotients : An introduction to methods of ring theory, 217, Springer (1975) MR0389953