Algebraic & Geometric Topology Volume 18, issue 5 (2018)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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The geometry of the knot concordance space

Tim D Cochran and Shelly Harvey

Algebraic & Geometric Topology 18 (2018) 2509–2540

DOI: 10.2140/agt.2018.18.2509

Bibliography

1	S Akbulut, R Kirby, Mazur manifolds, Michigan Math. J. 26 (1979) 259 MR544597
2	S Akbulut, K Yasui, Corks, plugs and exotic structures, J. Gökova Geom. Topol. 2 (2008) 40 MR2466001
3	L Bartholdi, R Grigorchuk, V Nekrashevych, From fractal groups to fractal sets, from: "Fractals in Graz 2001" (editors P Grabner, W Woess), Birkhäuser (2003) 25 MR2091700
4	S Boyer, Shake-slice knots and smooth contractible 4–manifolds, Math. Proc. Cambridge Philos. Soc. 98 (1985) 93 MR789723
5	M Brandenbursky, J Kędra, Concordance group and stable commutator length in braid groups, Algebr. Geom. Topol. 15 (2015) 2861 MR3426696
6	A Casson, M Freedman, Atomic surgery problems, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 181 MR780579
7	J C Cha, The structure of the rational concordance group of knots, 885, Amer. Math. Soc. (2007) MR2343079
8	T D Cochran, C W Davis, Counterexamples to Kauffman’s conjectures on slice knots, Adv. Math. 274 (2015) 263 MR3318151
9	T D Cochran, C W Davis, A Ray, Injectivity of satellite operators in knot concordance, J. Topol. 7 (2014) 948 MR3286894
10	T D Cochran, B D Franklin, M Hedden, P D Horn, Knot concordance and homology cobordism, Proc. Amer. Math. Soc. 141 (2013) 2193 MR3034445
11	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
12	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
13	T D Cochran, S Harvey, C Leidy, Primary decomposition and the fractal nature of knot concordance, Math. Ann. 351 (2011) 443 MR2836668
14	J Collins, On the concordance orders of knots, PhD thesis, University of Edinburgh (2012) arXiv:1206.0669
15	R H Fox, J W Milnor, Singularities of 2–spheres in 4–space and equivalence of knots, Bull. Amer. Math. Soc. 63 (1957) 406
16	R H Fox, J W Milnor, Singularities of 2–spheres in 4–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
17	M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
18	S L Harvey, Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group, Geom. Topol. 12 (2008) 387 MR2390349
19	M Hedden, P Kirk, Instantons, concordance, and Whitehead doubling, J. Differential Geom. 91 (2012) 281 MR2971290
20	C Kearton, The Milnor signatures of compound knots, Proc. Amer. Math. Soc. 76 (1979) 157 MR534409
21	R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology, II" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
22	P Kirk, C Livingston, Twisted knot polynomials: inversion, mutation and concordance, Topology 38 (1999) 663 MR1670424
23	A S Levine, Nonsurjective satellite operators and piecewise-linear concordance, Forum Math. Sigma 4 (2016) MR3589337
24	W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
25	C Livingston, The slicing number of a knot, Algebr. Geom. Topol. 2 (2002) 1051 MR1936979
26	C Livingston, The concordance genus of knots, Algebr. Geom. Topol. 4 (2004) 1 MR2031909
27	C Livingston, The stable 4-genus of knots, Algebr. Geom. Topol. 10 (2010) 2191 MR2745668
28	S Naik, Casson–Gordon invariants of genus one knots and concordance to reverses, J. Knot Theory Ramifications 5 (1996) 661 MR1414093
29	A Ray, Satellite operators with distinct iterates in smooth concordance, Proc. Amer. Math. Soc. 143 (2015) 5005 MR3391056
30	Y Sato, 3–dimensional homology handles and minimal second Betti numbers of 4–manifolds, Osaka J. Math. 35 (1998) 509 MR1648360
31	L R Taylor, On the genera of knots, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 144 MR547461
32	A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR0248854