Algebraic & Geometric Topology Volume 25, issue 4 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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On the nonorientable four-ball genus of torus knots

Fraser Binns, Sungkyung Kang, Jonathan Simone and Paula Truöl

Algebraic & Geometric Topology 25 (2025) 2209–2251

DOI: 10.2140/agt.2025.25.2209

Bibliography

1	S Allen, Nonorientable surfaces bounded by knots: a geography problem, New York J. Math. 29 (2023) 1038 MR4646147
2	W Ballinger, Concordance invariants from the E(−1) spectral sequence on Khovanov homology, preprint (2020) arXiv:2004.10807
3	J Batson, Nonorientable slice genus can be arbitrarily large, Math. Res. Lett. 21 (2014) 423 MR3272020
4	J Bodnár, D Celoria, M Golla, A note on cobordisms of algebraic knots, Algebr. Geom. Topol. 17 (2017) 2543 MR3686406
5	M Borodzik, J Hom, Involutive Heegaard Floer homology and rational cuspidal curves, Proc. Lond. Math. Soc. 118 (2019) 441 MR3932778
6	M Borodzik, C Livingston, Heegaard Floer homology and rational cuspidal curves, Forum Math. Sigma 2 (2014) MR3347955
7	B E Clark, Crosscaps and knots, Int. J. Math. Math. Sci. 1 (1978) 113 MR478131
8	D A Cox, Primes of the form x² + ny² : Fermat, class field theory and complex multiplication, Wiley (1989) MR1028322
9	A Daemi, C Scaduto, Chern–Simons functional, singular instantons, and the four-dimensional clasp number, J. Eur. Math. Soc. 26 (2024) 2127 MR4742808
10	I Dai, C Manolescu, Involutive Heegaard Floer homology and plumbed three-manifolds, J. Inst. Math. Jussieu 18 (2019) 1115 MR4021102
11	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4-manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
12	H Fan, Unoriented cobordism maps on link Floer homology, PhD thesis, University of California, Los Angeles (2019)
13	P Feller, M Golla, Non-orientable slice surfaces and inscribed rectangles, Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023) 1463 MR4675965
14	P Feller, D Krcatovich, On cobordisms between knots, braid index, and the upsilon-invariant, Math. Ann. 369 (2017) 301 MR3694648
15	P Feller, J Park, A Ray, On the upsilon invariant and satellite knots, Math. Z. 292 (2019) 1431 MR3980298
16	K A Frøyshov, Equivariant aspects of Yang–Mills Floer theory, Topology 41 (2002) 525 MR1910040
17	N Ghanbarian, The non-orientable 4-genus for knots with 10 crossings, J. Knot Theory Ramifications 31 (2022) 2250034 MR4450931
18	P M Gilmer, C Livingston, The nonorientable 4-genus of knots, J. Lond. Math. Soc. 84 (2011) 559 MR2855790
19	M Golla, M Marengon, Correction terms and the nonorientable slice genus, Michigan Math. J. 67 (2018) 59 MR3770853
20	S Gong, M Marengon, Nonorientable link cobordisms and torsion order in Floer homologies, Algebr. Geom. Topol. 23 (2023) 2627 MR4640136
21	C M Gordon, R A Litherland, On the signature of a link, Invent. Math. 47 (1978) 53 MR500905
22	C M Gordon, R A Litherland, K Murasugi, Signatures of covering links, Canadian J. Math. 33 (1981) 381 MR617628
23	M Hedden, On knot Floer homology and cabling, II, Int. Math. Res. Not. 2009 (2009) 2248 MR2511910
24	K Hendricks, C Manolescu, Involutive Heegaard Floer homology, Duke Math. J. 166 (2017) 1211 MR3649355
25	M Hogancamp, C Livingston, An involutive upsilon knot invariant, preprint (2017) arXiv:1710.08360
26	K Ireland, M Rosen, A classical introduction to modern number theory, 84, Springer (1990) MR1070716
27	S Jabuka, T Kelly, The nonorientable 4-genus for knots with 8 or 9 crossings, Algebr. Geom. Topol. 18 (2018) 1823 MR3784020
28	S Jabuka, C A Van Cott, Comparing nonorientable three genus and nonorientable four genus of torus knots, J. Knot Theory Ramifications 29 (2020) 2050013 MR4101607
29	S Jabuka, C A Van Cott, On a nonorientable analogue of the Milnor conjecture, Algebr. Geom. Topol. 21 (2021) 2571 MR4334520
30	A Juhász, Cobordisms of sutured manifolds and the functoriality of link Floer homology, Adv. Math. 299 (2016) 940 MR3519484
31	A Juhász, D Thurston, I Zemke, Naturality and mapping class groups in Heegard Floer homology, 1338, Amer. Math. Soc. (2021) MR4337438
32	A Juhász, I Zemke, New Heegaard Floer slice genus and clasp number bounds, preprint (2020) arXiv:2007.07106
33	P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, I, Topology 32 (1993) 773 MR1241873
34	J Levine, Polynomial invariants of knots of codimension two, Ann. of Math. 84 (1966) 537 MR200922
35	A Lobb, A counterexample to Batson’s conjecture, Math. Res. Lett. 26 (2019) 1789 MR4078695
36	V Longo, An infinite family of counterexamples to Batson’s conjecture, preprint (2020) arXiv:2011.00122
37	C Manolescu, B Owens, A concordance invariant from the Floer homology of double branched covers, Int. Math. Res. Not. 2007 (2007) MR2363303
38	L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR383406
39	H Murakami, A Yasuhara, Four-genus and four-dimensional clasp number of a knot, Proc. Amer. Math. Soc. 128 (2000) 3693 MR1690998
40	Y Ni, Z Wu, Cosmetic surgeries on knots in S³, J. Reine Angew. Math. 706 (2015) 1 MR3393360
41	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
42	P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
43	P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
44	J Rasmussen, Lens space surgeries and a conjecture of Goda and Teragaito, Geom. Topol. 8 (2004) 1013 MR2087076
45	W H Stevens, On the homology of branched cyclic covers of knots, PhD thesis, Louisiana State University and Agricultural & Mechanical College (1996) MR2694953
46	N Tairi, The smooth nonorientable 4-genus of an infinite family of torus knots, master’s thesis, Universität Bern (2020)
47	M Teragaito, Crosscap numbers of torus knots, Topology Appl. 138 (2004) 219 MR2035482
48	O Y Viro, Positioning in codimension 2, and the boundary, Uspehi Mat. Nauk 30 (1975) 231 MR420641
49	C T C Wall, Singular points of plane curves, 63, Cambridge Univ. Press (2004) MR2107253
50	S Wang, Semigroups of L-space knots and nonalgebraic iterated torus knots, Math. Res. Lett. 25 (2018) 335 MR3818626
51	A Yasuhara, Connecting lemmas and representing homology classes of simply connected 4-manifolds, Tokyo J. Math. 19 (1996) 245 MR1391941
52	I Zemke, Connected sums and involutive knot Floer homology, Proc. Lond. Math. Soc. 119 (2019) 214 MR3957835
53	I Zemke, Link cobordisms and functoriality in link Floer homology, J. Topol. 12 (2019) 94 MR3905679