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
Embedded surfaces with infinite cyclic knot group

Anthony Conway and Mark Powell

Geometry & Topology 27 (2023) 739–821
Bibliography
1 H Bass, Unitary algebraic K–theory, from: "Algebraic K–theory, III : Hermitian K–theory and geometric applications" (editor H Bass), Lecture Notes in Math. 343, Springer (1973) 57 MR0371994
2 R I Baykur, N Sunukjian, Knotted surfaces in 4–manifolds and stabilizations, J. Topol. 9 (2016) 215 MR3465848
3 M Borodzik, S Friedl, On the algebraic unknotting number, Trans. London Math. Soc. 1 (2014) 57 MR3296484
4 M Borodzik, S Friedl, The unknotting number and classical invariants, I, Algebr. Geom. Topol. 15 (2015) 85 MR3325733
5 S Boyer, Simply-connected 4–manifolds with a given boundary, Trans. Amer. Math. Soc. 298 (1986) 331 MR857447
6 J Boyle, Classifying 1–handles attached to knotted surfaces, Trans. Amer. Math. Soc. 306 (1988) 475 MR933302
7 G E Bredon, Topology and geometry, 139, Springer (1993) MR1224675
8 T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
9 A Conway, S Friedl, E Toffoli, The Blanchfield pairing of colored links, Indiana Univ. Math. J. 67 (2018) 2151 MR3900365
10 A Conway, M Powell, Characterisation of homotopy ribbon discs, Adv. Math. 391 (2021) MR4300918
11 D J Crowley, The classification of highly connected manifolds in dimensions 7 and 15, PhD thesis, Indiana University (2002) MR2703475
12 D Crowley, J Sixt, Stably diffeomorphic manifolds and l2q+1([π]), Forum Math. 23 (2011) 483 MR2805192
13 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
14 R Fintushel, R J Stern, Surfaces in 4–manifolds, Math. Res. Lett. 4 (1997) 907 MR1492129
15 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
16 S Friedl, C Leidy, M Nagel, M Powell, Twisted Blanchfield pairings and decompositions of 3-manifolds, Homology Homotopy Appl. 19 (2017) 275 MR3731479
17 S Friedl, M Nagel, P Orson, M Powell, A survey of the foundations of four-manifold theory in the topological category, preprint (2019) arXiv:1910.07372
18 S Friedl, M Powell, A calculation of Blanchfield pairings of 3–manifolds and knots, Mosc. Math. J. 17 (2017) 59 MR3634521
19 R E Gompf, A I Stipsicz, 4–Manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
20 I Hambleton, M Kreck, P Teichner, Topological 4–manifolds with geometrically two-dimensional fundamental groups, J. Topol. Anal. 1 (2009) 123 MR2541758
21 I Hambleton, P Teichner, A non-extended Hermitian form over [], Manuscripta Math. 93 (1997) 435 MR1465889
22 J A Hillman, A Kawauchi, Unknotting orientable surfaces in the 4–sphere, J. Knot Theory Ramifications 4 (1995) 213 MR1331748
23 J F P Hudson, Embeddings of bounded manifolds, Proc. Cambridge Philos. Soc. 72 (1972) 11 MR298679
24 A Juhász, M Miller, I Zemke, Transverse invariants and exotic surfaces in the 4–ball, Geom. Topol. 25 (2021) 2963 MR4347309
25 A Juház, I Zemke, Stabilization distance bounds from link Floer homology, preprint (2018) arXiv:1810.09158
26 D Kasprowski, M Powell, P Teichner, Algebraic criteria for stable diffeomorphism of spin 4–manifolds, preprint (2020) arXiv:2006.06127
27 A Kawauchi, Splitting a 4–manifold with infinite cyclic fundamental group, Osaka J. Math. 31 (1994) 489 MR1309399
28 A Kawauchi, Splitting a 4–manifold with infinite cyclic fundamental group, revised, J. Knot Theory Ramifications 22 (2013) MR3190119
29 Q Khan, Cancellation for 4–manifolds with virtually abelian fundamental group, Topology Appl. 220 (2017) 14 MR3619277
30 H J Kim, Modifying surfaces in 4–manifolds by twist spinning, Geom. Topol. 10 (2006) 27 MR2207789
31 H J Kim, D Ruberman, Smooth surfaces with non-simply-connected complements, Algebr. Geom. Topol. 8 (2008) 2263 MR2465741
32 H J Kim, D Ruberman, Topological triviality of smoothly knotted surfaces in 4–manifolds, Trans. Amer. Math. Soc. 360 (2008) 5869 MR2425695
33 R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 273 MR520548
34 M A Knus, Quadratic and Hermitian forms over rings, 294, Springer (1991) MR1096299
35 K H Ko, A Seifert-matrix interpretation of Cappell and Shaneson’s approach to link cobordisms, Math. Proc. Cambridge Philos. Soc. 106 (1989) 531 MR1010376
36 M Kreck, Isotopy classes of diffeomorphisms of (k1)–connected almost-parallelizable 2k–manifolds, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 643 MR561244
37 M Kreck, Surgery and duality, Ann. of Math. 149 (1999) 707 MR1709301
38 T Y Lam, Serre’s problem on projective modules, Springer (2006) MR2235330
39 J Levine, Knot modules, I, Trans. Amer. Math. Soc. 229 (1977) 1 MR461518
40 C Livingston, Surfaces bounding the unlink, Michigan Math. J. 29 (1982) 289 MR674282
41 B A Magurn, W van der Kallen, L N Vaserstein, Absolute stable rank and Witt cancellation for noncommutative rings, Invent. Math. 91 (1988) 525 MR928496
42 T E Mark, Knotted surfaces in 4–manifolds, Forum Math. 25 (2013) 597 MR3062865
43 T Oba, Surfaces in the 4–disk with the same boundary and fundamental group, Math. Res. Lett. 27 (2020) 265 MR4088816
44 B Perron, Pseudo-isotopies et isotopies en dimension quatre dans la catégorie topologique, Topology 25 (1986) 381 MR862426
45 F Quinn, Isotopy of 4–manifolds, J. Differential Geom. 24 (1986) 343 MR868975
46 A Ranicki, The algebraic theory of surgery, I : Foundations, Proc. London Math. Soc. 40 (1980) 87 MR560997
47 A Ranicki, Exact sequences in the algebraic theory of surgery, 26, Princeton Univ. Press (1981) MR620795
48 R Stong, Z Wang, Self-homeomorphisms of 4–manifolds with fundamental group , Topology Appl. 106 (2000) 49 MR1769331
49 N S Sunukjian, Surfaces in 4–manifolds : concordance, isotopy, and surgery, Int. Math. Res. Not. 2015 (2015) 7950 MR3404006