Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Band diagrams of immersed surfaces in $4$-manifolds

Mark Hughes, Seungwon Kim and Maggie Miller

Algebraic & Geometric Topology 25 (2025) 1731–1791
Bibliography
1 V I Arnold, A N Varchenko, S M Guseĭn-Zade, Особенности дифференцируемых отображении, Nauka (1982) 304 MR685918
2 R İ Baykur, N Sunukjian, Knotted surfaces in 4-manifolds and stabilizations, J. Topol. 9 (2016) 215 MR3465848
3 J S Carter, M Saito, Reidemeister moves for surface isotopies and their interpretation as moves to movies, J. Knot Theory Ramifications 2 (1993) 251 MR1238875
4 J S Carter, M Saito, Knotted surfaces and their diagrams, 55, Amer. Math. Soc. (1998) MR1487374
5 J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational problems in abstract algebra", Pergamon (1970) 329 MR258014
6 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
7 M H Freedman, F Quinn, Topology of 4-manifolds, 39, Princeton Univ. Press (1990) MR1201584
8 D Gay, R Kirby, Trisecting 4-manifolds, Geom. Topol. 20 (2016) 3097 MR3590351
9 A Hatcher, J Wagoner, Pseudo-isotopies of compact manifolds, 6, Soc. Math. France (1973) MR353337
10 C Hayashi, K Shimokawa, Heegaard splittings of trivial arcs in compression bodies, J. Knot Theory Ramifications 10 (2001) 71 MR1822141
11 M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242 MR119214
12 M W Hirsch, Differential topology, 33, Springer (1976) MR448362
13 F Hosokawa, A Kawauchi, Proposals for unknotted surfaces in four-spaces, Osaka Math. J. 16 (1979) 233 MR527028
14 M C Hughes, S Kim, M Miller, Isotopies of surfaces in 4-manifolds via banded unlink diagrams, Geom. Topol. 24 (2020) 1519 MR4157558
15 M Jabłonowski, Minimal generating sets of moves for surfaces immersed in the four-space, J. Knot Theory Ramifications 32 (2023) 2350071 MR4683263
16 J M Joseph, M R Klug, B M Ruppik, H R Schwartz, Unknotting numbers of 2-spheres in the 4-sphere, J. Topol. 14 (2021) 1321 MR4332491
17 S Kamada, 2-dimensional braids and chart descriptions, from: "Topics in knot theory", NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 399, Kluwer (1993) 277 MR1257915
18 S Kamada, Unknotting immersed surface-links and singular 2-dimensional braids by 1-handle surgeries, Osaka J. Math. 36 (1999) 33 MR1670738
19 S Kamada, Braid and knot theory in dimension four, 95, Amer. Math. Soc. (2002) MR1900979
20 S Kamada, A Kawauchi, J Kim, S Y Lee, Presentation of immersed surface-links by marked graph diagrams, J. Knot Theory Ramifications 27 (2018) 1850052 MR3855473
21 A Kawauchi, T Shibuya, S Suzuki, Descriptions on surfaces in four-space, I : Normal forms, Math. Sem. Notes Kobe Univ. 10 (1982) 75 MR672939
22 C Kearton, V Kurlin, All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron, Algebr. Geom. Topol. 8 (2008) 1223 MR2443242
23 F Laudenbach, Sur les 2-sphères d’une variété de dimension 3, Ann. of Math. 97 (1973) 57 MR314054
24 F Laudenbach, V Poénaru, A note on 4-dimensional handlebodies, Bull. Soc. Math. France 100 (1972) 337 MR317343
25 J Meier, T Schirmer, A Zupan, Classification of trisections and the generalized property R conjecture, Proc. Amer. Math. Soc. 144 (2016) 4983 MR3544545
26 J Meier, A Zupan, Bridge trisections of knotted surfaces in S4, Trans. Amer. Math. Soc. 369 (2017) 7343 MR3683111
27 J Meier, A Zupan, Bridge trisections of knotted surfaces in 4-manifolds, Proc. Natl. Acad. Sci. USA 115 (2018) 10880 MR3871791
28 M Miller, P Naylor, Trisections of nonorientable 4-manifolds, Michigan Math. J. 74 (2024) 403 MR4739421
29 D Roseman, Reidemeister-type moves for surfaces in four-dimensional space, from: "Knot theory", Banach Center Publ. 42, Polish Acad. Sci. Inst. Math. (1998) 347 MR1634466
30 R Schneiderman, P Teichner, The group of disjoint 2-spheres in 4-space, Ann. of Math. 190 (2019) 669 MR4024561
31 S Smale, A classification of immersions of the two-sphere, Trans. Amer. Math. Soc. 90 (1958) 281 MR104227
32 F J Swenton, On a calculus for 2-knots and surfaces in 4-space, J. Knot Theory Ramifications 10 (2001) 1133 MR1871221