Volume 24, issue 3 (2020)

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

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Isotopies of surfaces in $4$–manifolds via banded unlink diagrams

Mark C Hughes, Seungwon Kim and Maggie Miller

Geometry & Topology 24 (2020) 1519–1569
Bibliography
1 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
2 J S Carter, M Saito, Knotted surfaces and their diagrams, 55, Amer. Math. Soc. (1998) MR1487374
3 I Dai, M Miller, The 0–concordance monoid is infinitely generated, preprint (2019) arXiv:1907.07166
4 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR679066
5 D Gabai, The 4–dimensional light bulb theorem, J. Amer. Math. Soc. 33 (2020) 609 MR4127900
6 D Gay, R Kirby, Trisecting 4–manifolds, Geom. Topol. 20 (2016) 3097 MR3590351
7 H Gluck, The embedding of two-spheres in the four-sphere, Trans. Amer. Math. Soc. 104 (1962) 308 MR146807
8 C M Gordon, Knots in the 4–sphere, Comment. Math. Helv. 51 (1976) 585 MR440561
9 K Habiro, Y Marumoto, Y Yamada, Gluck surgery and framed links in 4–manifolds, from: "Knots in Hellas ’98" (editors C M Gordon, V F R Jones, L H Kauffman, S Lambropoulou, J H Przytycki), Ser. Knots Everything 24, World Sci. (2000) 80 MR1865702
10 J Joseph, 0–Concordance of knotted surfaces and Alexander ideals, preprint (2019) arXiv:1911.13112
11 S Kamada, Nonorientable surfaces in 4–space, Osaka J. Math. 26 (1989) 367 MR1017592
12 S Kamada, 2–Dimensional braids and chart descriptions, from: "Topics in knot theory" (editor M E Bozhüyük), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 399, Kluwer (1993) 277 MR1257915
13 S Kamada, Braid and knot theory in dimension four, 95, Amer. Math. Soc. (2002) MR1900979
14 A Kawauchi, A chord diagram of a ribbon surface-link, J. Knot Theory Ramifications 24 (2015) MR3402895
15 A Kawauchi, T Shibuya, S Suzuki, Descriptions on surfaces in four-space, I : Normal forms, Math. Sem. Notes Kobe Univ. 10 (1982) 75 MR672939
16 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
17 R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
18 F Laudenbach, V Poénaru, A note on 4–dimensional handlebodies, Bull. Soc. Math. France 100 (1972) 337 MR317343
19 R A Litherland, Deforming twist-spun knots, Trans. Amer. Math. Soc. 250 (1979) 311 MR530058
20 J Meier, T Schirmer, A Zupan, Classification of trisections and the generalized property R conjecture, Proc. Amer. Math. Soc. 144 (2016) 4983 MR3544545
21 J Meier, A Zupan, Bridge trisections of knotted surfaces in S4, Trans. Amer. Math. Soc. 369 (2017) 7343 MR3683111
22 J Meier, A Zupan, Bridge trisections of knotted surfaces in 4-manifolds, Proc. Natl. Acad. Sci. USA 115 (2018) 10880 MR3871791
23 P M Melvin, Blowing up and down in 4–manifolds, PhD thesis, University of California, Berkeley (1977) MR2627246
24 K Miyazaki, Band-sums are ribbon concordant to the connected sum, Proc. Amer. Math. Soc. 126 (1998) 3401 MR1451821
25 D Nash, A I Stipsicz, Gluck twist on a certain family of 2–knots, Michigan Math. J. 61 (2012) 703 MR3049286
26 D Roseman, Reidemeister-type moves for surfaces in four-dimensional space, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42, Polish Acad. Sci. Inst. Math. (1998) 347 MR1634466
27 N S Sunukjian, Surfaces in 4–manifolds : concordance, isotopy, and surgery, Int. Math. Res. Not. 2015 (2015) 7950 MR3404006
28 N Sunukjian, 0–Concordance of 2–knots, preprint (2019) arXiv:1907.06524
29 F J Swenton, On a calculus for 2–knots and surfaces in 4–space, J. Knot Theory Ramifications 10 (2001) 1133 MR1871221
30 M Teragaito, Twist-roll spun knots, Proc. Amer. Math. Soc. 122 (1994) 597 MR1201806
31 T Yanagawa, On ribbon 2–knots : the 3–manifold bounded by the 2–knots, Osaka Math. J. 6 (1969) 447 MR266193
32 K Yoshikawa, On a 2–knot group with nontrivial center, Bull. Austral. Math. Soc. 25 (1982) 321 MR671481
33 K Yoshikawa, An enumeration of surfaces in four-space, Osaka J. Math. 31 (1994) 497 MR1309400
34 E C Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965) 471 MR195085
35 A Zupan, Bridge and pants complexities of knots, J. Lond. Math. Soc. 87 (2013) 43 MR3022706