Volume 9, issue 1 (2009)

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The concordance genus of a knot, II

Charles Livingston

Algebraic & Geometric Topology 9 (2009) 167–185
Bibliography
1 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
2 J C Cha, C Livingston, KnotInfo
3 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
4 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
5 D S Dummit, R M Foote, Abstract algebra, John Wiley & Sons (2004) MR2286236
6 R H Fox, Free differential calculus. III. Subgroups, Ann. of Math. $(2)$ 64 (1956) 407 MR0095876
7 R H Fox, J W Milnor, Singularities of $2$–spheres in $4$–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
8 C M Gordon, Some aspects of classical knot theory, from: "Knot theory (Proc. Sem., Plans-sur-Bex, 1977)" (editor J C Hausmann), Lecture Notes in Math. 685, Springer (1978) 1 MR521730
9 J E Grigsby, D Ruberman, S Strle, Knot concordance and Heegaard Floer homology invariants in branched covers, Geom. Topol. 12 (2008) 2249 MR2443966
10 C Herald, P Kirk, C Livingston, Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation arXiv:0804.1355
11 S Jabuka, S Naik, Order in the concordance group and Heegaard Floer homology, Geom. Topol. 11 (2007) 979 MR2326940
12 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
13 J Levine, Invariants of knot cobordism, Invent. Math. 8 $(1969)$ 98–110; addendum, ibid. 8 (1969) 355 MR0253348
14 P Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007) 2141 MR2366190
15 C Livingston, The algebraic concordance order of a knot arXiv:0806.3068
16 C Livingston, The concordance genus of knots, Algebr. Geom. Topol. 4 (2004) 1 MR2031909
17 C Livingston, S Naik, Obstructing four-torsion in the classical knot concordance group, J. Differential Geom. 51 (1999) 1 MR1703602
18 J Milnor, D Husemoller, Symmetric bilinear forms, Ergebnisse der Math. und ihrer Grenzgebiete 73, Springer (1973) MR0506372
19 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
20 Y Nakanishi, A note on unknotting number, Math. Sem. Notes Kobe Univ. 9 (1981) 99 MR634000
21 P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
22 A Plans, Contribution to the study of the homology groups of the cyclic ramified coverings corresponding to a knot, Revista Acad. Ci. Madrid 47 (1953) 161 MR0056923
23 J Rasmussen, Khovanov homology and the slice genus arXiv:math.GT/0402131
24 D Rolfsen, Knots and links, Math. Lecture Ser. 7, Publish or Perish (1976) MR0515288
25 W Scharlau, Quadratic and Hermitian forms, Grund. der Math. Wissenschaften 270, Springer (1985) MR770063
26 J P Serre, A course in arithmetic, Graduate Texts in Math. 7, Springer (1973) MR0344216
27 N W Stoltzfus, Unraveling the integral knot concordance group, Mem. Amer. Math. Soc. 12 (1977) MR0467764
28 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR0248854