Volume 18, issue 3 (2018)

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The nonorientable $4\mskip-1.5mu $–genus for knots with $8$ or $9$ crossings

Stanislav Jabuka and Tynan Kelly

Algebraic & Geometric Topology 18 (2018) 1823–1856
Bibliography
1 J Batson, Nonorientable slice genus can be arbitrarily large, Math. Res. Lett. 21 (2014) 423 MR3272020
2 J Cha, C Livingston, KnotInfo: table of knot invariants, electronic reference
3 B E Clark, Crosscaps and knots, Internat. J. Math. Math. Sci. 1 (1978) 113 MR0478131
4 J Collins, P Kirk, C Livingston, The concordance classification of low crossing number knots, Proc. Amer. Math. Soc. 143 (2015) 4525 MR3373950
5 J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational problems in abstract algebra" (editor J Leech), Pergamon (1970) 329 MR0258014
6 S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
7 A L Edmonds, Least area Seifert surfaces and periodic knots, Topology Appl. 18 (1984) 109 MR769284
8 R H Fox, A quick trip through knot theory, from: "Topology of 3–manifolds and related topics" (editor M K Fort), Prentice-Hall (1962) 120 MR0140099
9 R H Fox, Some problems in knot theory, from: "Topology of 3–manifolds and related topics" (editor M K Fort), Prentice-Hall (1962) 168 MR0140100
10 R H Fox, J W Milnor, Singularities of 2–spheres in 4–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
11 P M Gilmer, On the slice genus of knots, Invent. Math. 66 (1982) 191 MR656619
12 P M Gilmer, C Livingston, The nonorientable 4–genus of knots, J. Lond. Math. Soc. 84 (2011) 559 MR2855790
13 L Goeritz, Knoten und quadratische Formen, Math. Z. 36 (1933) 647 MR1545364
14 C M Gordon, R A Litherland, On the signature of a link, Invent. Math. 47 (1978) 53 MR0500905
15 J E Greene, Alternating links and definite surfaces, Duke Math. J. 166 (2017) 2133 MR3694566
16 L Guillou, A Marin, Une extension d’un théorème de Rohlin sur la signature, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 97 MR900247
17 R Kirby, P Melvin, Local surgery formulas for quantum invariants and the Arf invariant, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7, Geom. Topol. Publ. (2004) 213 MR2172485
18 C Livingston, The slicing number of a knot, Algebr. Geom. Topol. 2 (2002) 1051 MR1936979
19 Y Matsumoto, An elementary proof of Rochlin’s signature theorem and its extension by Guillou and Marin, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 119 MR900248
20 H Murakami, A Yasuhara, Four-genus and four-dimensional clasp number of a knot, Proc. Amer. Math. Soc. 128 (2000) 3693 MR1690998
21 B Owens, On slicing invariants of knots, Trans. Amer. Math. Soc. 362 (2010) 3095 MR2592947
22 B Owens, S Strle, Rational homology spheres and the four-ball genus of knots, Adv. Math. 200 (2006) 196 MR2199633
23 B Owens, S Strle, Immersed disks, slicing numbers and concordance unknotting numbers, Comm. Anal. Geom. 24 (2016) 1107 MR3622316
24 P S Ozsváth, A I Stipsicz, Z Szabó, Concordance homomorphisms from knot Floer homology, Adv. Math. 315 (2017) 366 MR3667589
25 P S Ozsváth, A I Stipsicz, Z Szabó, Unoriented knot Floer homology and the unoriented four-ball genus, Int. Math. Res. Not. 2017 (2017) 5137 MR3694597
26 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
27 M Scharlemann, Crossing changes, Chaos Solitons Fractals 9 (1998) 693 MR1628751
28 H Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935) 571 MR1512955
29 T Shibuya, Some relations among various numerical invariants for links, Osaka J. Math. 11 (1974) 313 MR0353295
30 O J Viro, Positioning in codimension 2, and the boundary, Uspehi Mat. Nauk 30 (1975) 231 MR0420641
31 A Yasuhara, Connecting lemmas and representing homology classes of simply connected 4–manifolds, Tokyo J. Math. 19 (1996) 245 MR1391941