Volume 17, issue 4 (2013)

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

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Filtering smooth concordance classes of topologically slice knots

Tim D Cochran, Shelly Harvey and Peter Horn

Geometry & Topology 17 (2013) 2103–2162
Bibliography
1 S Akbulut, R Kirby, Branched covers of surfaces in $4$–manifolds, Math. Ann. 252 (1979/80) 111 MR593626
2 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
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, Topological minimal genus and $L^2$–signatures, Algebr. Geom. Topol. 8 (2008) 885 MR2443100
5 J C Cha, Amenable $L^{2}$–theoretic methods and knot concordance, Inter. Math. Res. Notices (2013)
6 T D Cochran, R E Gompf, Applications of Donaldson's theorems to classical knot concordance, homology $3$–spheres and property $P$, Topology 27 (1988) 495 MR976591
7 T Cochran, S Harvey, C Leidy, Link concordance and generalized doubling operators, Algebr. Geom. Topol. 8 (2008) 1593 MR2443256
8 T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
9 T D Cochran, S Harvey, C Leidy, 2–torsion in the $n$–solvable filtration of the knot concordance group, Proc. Lond. Math. Soc. 102 (2011) 257 MR2769115
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, W B R Lickorish, Unknotting information from $4$–manifolds, Trans. Amer. Math. Soc. 297 (1986) 125 MR849471
12 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. 157 (2003) 433 MR1973052
13 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
14 C W Davis, Linear independence of knots arising from iterated infection without the use of Tristram–Levine signature, Int. Math. Res. Not. 2013 (2013)
15 S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
16 N D Elkies, A characterization of the $\mathbf{Z}^n$ lattice, Math. Res. Lett. 2 (1995) 321 MR1338791
17 H Endo, Linear independence of topologically slice knots in the smooth cobordism group, Topology Appl. 63 (1995) 257 MR1334309
18 R Fintushel, R J Stern, Pseudofree orbifolds, Ann. of Math. 122 (1985) 335 MR808222
19 R Fintushel, R J Stern, Instanton homology of Seifert fibred homology three spheres, Proc. London Math. Soc. 61 (1990) 109 MR1051101
20 M H Freedman, F Quinn, Topology of $4$–manifolds, Princeton Mathematical Series 39, Princeton Univ. Press (1990) MR1201584
21 M Furuta, Homology cobordism group of homology $3$–spheres, Invent. Math. 100 (1990) 339 MR1047138
22 P M Gilmer, Configurations of surfaces in $4$–manifolds, Trans. Amer. Math. Soc. 264 (1981) 353 MR603768
23 P M Gilmer, C Livingston, On surgery curves for genus one slice knots, to appear in Pacific Journal Math.
24 P Gilmer, C Livingston, The Casson–Gordon invariant and link concordance, Topology 31 (1992) 475 MR1174253
25 P Gilmer, C Livingston, Discriminants of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 112 (1992) 127 MR1162937
26 R E Gompf, Smooth concordance of topologically slice knots, Topology 25 (1986) 353 MR842430
27 R E Gompf, A I Stipsicz, $4$–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, Amer. Math. Soc. (1999) MR1707327
28 C M Gordon, Some aspects of classical knot theory, from: "Knot theory" (editor J C Hausmann), Lecture Notes in Math. 685, Springer (1978) 1 MR521730
29 J Greene, S Jabuka, The slice-ribbon conjecture for $3$–stranded pretzel knots, Amer. J. Math. 133 (2011) 555 MR2808326
30 J E Grigsby, D Ruberman, S Strle, Knot concordance and Heegaard Floer homology invariants in branched covers, Geom. Topol. 12 (2008) 2249 MR2443966
31 M Hedden, Knot Floer homology of Whitehead doubles, Geom. Topol. 11 (2007) 2277 MR2372849
32 M Hedden, S G Kim, C Livingston, Topologically slice knots of smooth concordance order two arXiv:1212.6628
33 M Hedden, P Kirk, Instantons, concordance, and Whitehead doubling, J. Differential Geom. 91 (2012) 281 MR2971290
34 M Hedden, C Livingston, D Ruberman, Topologically slice knots with nontrivial Alexander polynomial, Adv. Math. 231 (2012) 913 MR2955197
35 J Hom, The knot Floer complex and the smooth concordance group, to appear in Comm. Math. Helv. arXiv:1111.6635
36 J Hoste, A formula for Casson's invariant, Trans. Amer. Math. Soc. 297 (1986) 547 MR854084
37 S Jabuka, Concordance invariants from higher order covers, Topology Appl. 159 (2012) 2694 MR2923439
38 S Jabuka, S Naik, Order in the concordance group and Heegaard Floer homology, Geom. Topol. 11 (2007) 979 MR2326940
39 P B Kronheimer, T S Mrowka, Gauge theory and Rasmussen's invariant, Journal of Topology (2013)
40 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 327 MR780587
41 C Manolescu, B Owens, A concordance invariant from the Floer homology of double branched covers, Int. Math. Res. Not. 2007 (2007) 21 MR2363303
42 B Owens, S Strle, Rational homology spheres and the four-ball genus of knots, Adv. Math. 200 (2006) 196 MR2199633
43 B Owens, S Strle, A characterization of the $\mathbb Z^n\oplus\mathbb Z(\delta)$ lattice and definite nonunimodular intersection forms, Amer. J. Math. 134 (2012) 891 MR2956253
44 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
45 P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
46 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
47 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
48 P S Ozsváth, Z Szabó, Knot Floer homology and integer surgeries, Algebr. Geom. Topol. 8 (2008) 101 MR2377279
49 J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
50 V A Rohlin, Two-dimensional submanifolds of four-dimensional manifolds, Funkcional. Anal. i Priložen. 5 (1971) 48 MR0298684
51 D Ruberman, S Strle, Concordance properties of parallel links arXiv:1108.4476
52 A Scorpan, The wild world of $4$–manifolds, Amer. Math. Soc. (2005) MR2136212
53 O J Viro, Branched coverings of manifolds with boundary, and invariants of links, I, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 1241 MR0370605