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Whitney towers, gropes and Casson–Gordon style invariants of links

Min Hoon Kim

Algebraic & Geometric Topology 15 (2015) 1813–1845
Bibliography
1 R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. 65 (1957) 340 MR0085512
2 J R Burke, Infection by string links and new structure in the knot concordance group, Algebr. Geom. Topol. 14 (2014) 1577 MR3212578
3 A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 39 MR520521
4 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
5 J C Cha, Structure of the string link concordance group and Hirzebruch-type invariants, Indiana Univ. Math. J. 58 (2009) 891 MR2514393
6 J C Cha, Link concordance, homology cobordism and Hirzebruch-type defects from iterated $p$–covers, J. Eur. Math. Soc. (JEMS) 12 (2010) 555 MR2639313
7 J C Cha, Amenable $L^2$–theoretic methods and knot concordance, Int. Math. Res. Not. 2014 (2014) 4768 MR3257550
8 J C Cha, Symmetric Whitney tower cobordism for bordered $3$–manifolds and links, Trans. Amer. Math. Soc. 366 (2014) 3241 MR3180746
9 J C Cha, M Powell, Nonconcordant links with homology cobordant zero-framed surgery manifolds, Pacific J. Math. 272 (2014) 1 MR3270170
10 D Cimasoni, A geometric construction of the Conway potential function, Comment. Math. Helv. 79 (2004) 124 MR2031702
11 T D Cochran, S Harvey, C Leidy, Link concordance and generalized doubling operators, Algebr. Geom. Topol. 8 (2008) 1593 MR2443256
12 T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
13 T D Cochran, S Harvey, C Leidy, Primary decomposition and the fractal nature of knot concordance, Math. Ann. 351 (2011) 443 MR2836668
14 T D Cochran, T Kim, Higher-order Alexander invariants and filtrations of the knot concordance group, Trans. Amer. Math. Soc. 360 (2008) 1407 MR2357701
15 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. 157 (2003) 433 MR1973052
16 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
17 T D Cochran, P Teichner, Knot concordance and von Neumann $\rho$–invariants, Duke Math. J. 137 (2007) 337 MR2309149
18 J Conant, R Schneiderman, P Teichner, Higher-order intersections in low-dimensional topology, Proc. Natl. Acad. Sci. USA 108 (2011) 8131 MR2806650
19 D Cooper, The universal abelian cover of a link, from: "Low-dimensional topology" (editors R Brown, T L Thickstun), London Math. Soc. Lecture Note Ser. 48, Cambridge Univ. Press (1982) 51 MR662427
20 R H Crowell, R H Fox, Introduction to knot theory, Graduate Texts in Math. 57, Springer (1977) MR0445489
21 C W Davis, Von Neumann rho-invariants and torsion in the topological knot concordance group, Algebr. Geom. Topol. 12 (2012) 753 MR2914617
22 B D Franklin, The effect of infecting curves on knot concordance, Int. Math. Res. Not. 2013 (2013) 184 MR3041699
23 M H Freedman, F Quinn, Topology of $4$–manifolds, Princeton Math. Series 39, Princeton Univ. Press (1990) MR1201584
24 S Friedl, M Powell, An injectivity theorem for Casson–Gordon type representations relating to the concordance of knots and links, Bull. Korean Math. Soc. 49 (2012) 395 MR2934490
25 S Friedl, M Powell, Links not concordant to the Hopf link, Math. Proc. Cambridge Philos. Soc. 156 (2014) 425 MR3181634
26 S L Harvey, Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group, Geom. Topol. 12 (2008) 387 MR2390349
27 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
28 J Hillman, Algebraic invariants of links, Series on knots and everything 52, World Scientific Publishing Co. Pte. Ltd. (2012) MR2931688
29 P D Horn, The nontriviality of the grope filtrations of the knot and link concordance groups, Comment. Math. Helv. 85 (2010) 751 MR2718138
30 A Kawauchi, On the Alexander polynomials of cobordant links, Osaka J. Math. 15 (1978) 151 MR0488022
31 C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. 10 (1975) 406 MR0385873
32 J P Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
33 J P Levine, The module of a $2$–component link, Comment. Math. Helv. 57 (1982) 377 MR689070
34 J P Levine, Link invariants via the eta-invariant, Comment. Math. Helv. 69 (1994) 82 MR1259607
35 R Schneiderman, Whitney towers and gropes in $4$–manifolds, Trans. Amer. Math. Soc. 358 (2006) 4251 MR2231378