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A lower bound on the stable $4$–genus of knots

Damian Iltgen

Algebraic & Geometric Topology 22 (2022) 2239–2265
Bibliography
1 S Baader, L Lewark, The stable 4–genus of alternating knots, Asian J. Math. 21 (2017) 1183 MR3778124
2 A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, 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 A Conway, Algebraic concordance and Casson–Gordon invariants, technical note (2017)
5 A Conway, S Friedl, G Herrmann, Linking forms revisited, Pure Appl. Math. Q. 12 (2016) 493 MR3842851
6 C W Davis, Von Neumann rho invariants and torsion in the topological knot concordance group, Algebr. Geom. Topol. 12 (2012) 753 MR2914617
7 M H Freedman, The disk theorem for four-dimensional manifolds, from: "Proceedings of the International Congress of Mathematicians" (editors Z Ciesielski, C a Olech), PWN (1984) 647 MR804721
8 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
9 P M Gilmer, On the slice genus of knots, Invent. Math. 66 (1982) 191 MR656619
10 P M Gilmer, Slice knots in S3, Quart. J. Math. Oxford Ser. 34 (1983) 305 MR711523
11 P Gilmer, Classical knot and link concordance, Comment. Math. Helv. 68 (1993) 1 MR1201199
12 S G Kim, Polynomial splittings of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 59 MR2127228
13 J Levine, Invariants of knot cobordism, Invent. Math. 8 (1969) 98 MR253348
14 P Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007) 2141 MR2366190
15 R A Litherland, Signatures of iterated torus knots, from: "Topology of low-dimensional manifolds" (editor R A Fenn), Lecture Notes in Math. 722, Springer (1979) 71 MR547456
16 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math., Amer. Math. Soc. (1984) 327 MR780587
17 C Livingston, The stable 4–genus of knots, Algebr. Geom. Topol. 10 (2010) 2191 MR2745668
18 C Livingston, S Naik, Introduction to knot concordance, work in progress
19 C Livingston, S Naik, Obstructing four-torsion in the classical knot concordance group, J. Differential Geom. 51 (1999) 1 MR1703602
20 C Livingston, S Naik, Knot concordance and torsion, Asian J. Math. 5 (2001) 161 MR1868169
21 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR171275
22 S Naik, Casson–Gordon invariants of genus one knots and concordance to reverses, J. Knot Theory Ramifications 5 (1996) 661 MR1414093
23 P J Rippon, H Taylor, Even and odd periods in continued fractions of square roots, Fibonacci Quart. 42 (2004) 170 MR2071782
24 A Tamulis, Knots of ten or fewer crossings of algebraic order 2, J. Knot Theory Ramifications 11 (2002) 211 MR1895371
25 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR248854