Algebraic & Geometric Topology Volume 25, issue 3 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Bridge trisections and Seifert solids

Jason Joseph, Jeffrey Meier, Maggie Miller and Alexander Zupan

Algebraic & Geometric Topology 25 (2025) 1501–1522

DOI: 10.2140/agt.2025.25.1501

Bibliography

1	S Bleiler, M Scharlemann, A projective plane in ℝ⁴ with three critical points is standard : strongly invertible knots have property P, Topology 27 (1988) 519 MR976593
2	J S Carter, M Saito, A Seifert algorithm for knotted surfaces, Topology 36 (1997) 179 MR1410470
3	T Cochran, Ribbon knots in S⁴, J. Lond. Math. Soc. 28 (1983) 563 MR724727
4	I Dai, M Miller, The 0-concordance monoid admits an infinite linearly independent set, Proc. Amer. Math. Soc. 151 (2023) 3601 MR4591791
5	D Gay, R Kirby, Trisecting 4-manifolds, Geom. Topol. 20 (2016) 3097 MR3590351
6	H Gluck, The embedding of two-spheres in the four-sphere, Trans. Amer. Math. Soc. 104 (1962) 308 MR146807
7	C M Gordon, Knots in the 4-sphere, Comment. Math. Helv. 51 (1976) 585 MR440561
8	C M Gordon, R A Litherland, On the signature of a link, Invent. Math. 47 (1978) 53 MR500905
9	J Joseph, J Meier, M Miller, A Zupan, Bridge trisections and classical knotted surface theory, Pacific J. Math. 319 (2022) 343 MR4482720
10	A Kawauchi, T Shibuya, S Suzuki, Descriptions on surfaces in four-space, I : Normal forms, Math. Sem. Notes Kobe Univ. 10 (1982) 75 MR672939
11	M Kobayashi, T Kobayashi, On canonical genus and free genus of knot, J. Knot Theory Ramifications 5 (1996) 77 MR1373811
12	C Livingston, Surfaces bounding the unlink, Michigan Math. J. 29 (1982) 289 MR674282
13	J Meier, T Schirmer, A Zupan, Classification of trisections and the generalized property R conjecture, Proc. Amer. Math. Soc. 144 (2016) 4983 MR3544545
14	J Meier, A Thompson, A Zupan, Cubic graphs induced by bridge trisections, Math. Res. Lett. 30 (2023) 1207 MR4728442
15	J Meier, A Zupan, Bridge trisections of knotted surfaces in S⁴, Trans. Amer. Math. Soc. 369 (2017) 7343 MR3683111
16	J Meier, A Zupan, Bridge trisections of knotted surfaces in 4-manifolds, Proc. Natl. Acad. Sci. USA 115 (2018) 10880 MR3871791
17	K Miyazaki, On the relationship among unknotting number, knotting genus and Alexander invariant for 2-knots, Kobe J. Math. 3 (1986) 77 MR867806
18	Y Moriah, On the free genus of knots, Proc. Amer. Math. Soc. 99 (1987) 373 MR870804
19	M Scharlemann, Smooth spheres in ℝ⁴ with four critical points are standard, Invent. Math. 79 (1985) 125 MR774532
20	C M Tsau, A note on incompressible surfaces in solid tori and in lens spaces, from: "Knots 90", de Gruyter (1992) 213 MR1177425
21	R Weidmann, On the rank of amalgamated products and product knot groups, Math. Ann. 312 (1998) 761 MR1660235
22	T Yanagawa, On ribbon 2-knots : the 3-manifold bounded by the 2-knots, Osaka Math. J. 6 (1969) 447 MR266193
23	E C Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965) 471 MR195085
24	A Zupan, Bridge and pants complexities of knots, J. Lond. Math. Soc. 87 (2013) 43 MR3022706