Algebraic & Geometric Topology Volume 10, issue 4 (2010)

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The stable $4$–genus of knots

Charles Livingston

Algebraic & Geometric Topology 10 (2010) 2191–2202

DOI: 10.2140/agt.2010.10.2191

Bibliography

1	C Bavard, Longueur stable des commutateurs, Enseign. Math. $(2)$ 37 (1991) 109 MR1115747
2	D Calegari, scl, MSJ Memoirs 20, Mathematical Society of Japan (2009) MR2527432
3	D Calegari, Stable commutator length is rational in free groups, J. Amer. Math. Soc. 22 (2009) 941 MR2525776
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	R H Fox, J W Milnor, Singularities of $2$–spheres in $4$-space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
6	P M Gilmer, On the slice genus of knots, Invent. Math. 66 (1982) 191 MR656619
7	P M Gilmer, Slice knots in $S^{3}$, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 305 MR711523
8	P M Gilmer, C Livingston, The Casson–Gordon invariant and link concordance, Topology 31 (1992) 475 MR1174253
9	J Levine, Invariants of knot cobordism, Invent. Math. 8 $(1969)$, 98–110; addendum, ibid. 8 (1969) 355 MR0253348
10	R Litherland, The $4$–genus of connected sums of $(2,k)$–torus knots, personal communication (2009)
11	K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
12	P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
13	J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419
14	A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR0248854
15	D Zhuang, Irrational stable commutator length in finitely presented groups, J. Mod. Dyn. 2 (2008) 499 MR2417483