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

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

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 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Embedding surfaces in $4$–manifolds

Daniel Kasprowski, Mark Powell, Arunima Ray and Peter Teichner

Geometry & Topology 28 (2024) 2399–2482
Bibliography
1 M Aït Nouh, Genera and degrees of torus knots in P2, J. Knot Theory Ramifications 18 (2009) 1299 MR2569563
2 S Behrens, B Kalmár, M H Kim, M Powell, A Ray, editors, The disc embedding theorem, Oxford Univ. Press (2021) MR4519498
3 A J Casson, Three lectures on new-infinite constructions in 4–dimensional manifolds, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 201 MR0900253
4 T D Cochran, A Ray, Shake slice and shake concordant knots, J. Topol. 9 (2016) 861 MR3551841
5 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L2–signatures, Ann. of Math. 157 (2003) 433 MR1973052
6 J Conant, R Schneiderman, P Teichner, Universal quadratic forms and Whitney tower intersection invariants, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18, Geom. Topol. Publ. (2012) 35 MR3084231
7 J Conant, R Schneiderman, P Teichner, Whitney tower concordance of classical links, Geom. Topol. 16 (2012) 1419 MR2967057
8 J Conant, R Schneiderman, P Teichner, Milnor invariants and twisted Whitney towers, J. Topol. 7 (2014) 187 MR3180617
9 R Connelly, A new proof of Brown’s collaring theorem, Proc. Amer. Math. Soc. 27 (1971) 180 MR0267588
10 P Feller, A N Miller, M Nagel, P Orson, M Powell, A Ray, Embedding spheres in knot traces, Compos. Math. 157 (2021) 2242 MR4328000
11 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR0679066
12 M Freedman, R Kirby, A geometric proof of Rochlin’s theorem, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 85 MR0520525
13 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
14 P M Gilmer, Configurations of surfaces in 4–manifolds, Trans. Amer. Math. Soc. 264 (1981) 353 MR603768
15 M Golubitsky, V Guillemin, Stable mappings and their singularities, 14, Springer (1973) MR0341518
16 L Guillou, A Marin, Une extension d’un théorème de Rohlin sur la signature, from: "Seminar on real algebraic geometry" (editor J J Risler), Publ. Math. Univ. Paris VII 9, Univ. Paris VII (1980) 69 MR0700837
17 I Hambleton, M Kreck, Cancellation of hyperbolic forms and topological four-manifolds, J. Reine Angew. Math. 443 (1993) 21 MR1241127
18 M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
19 D Kasprowski, M Land, M Powell, P Teichner, Stable classification of 4–manifolds with 3–manifold fundamental groups, J. Topol. 10 (2017) 827 MR3797598
20 D Kasprowski, M Powell, P Teichner, Algebraic criteria for stable diffeomorphism of spin 4–manifolds, preprint (2020) arXiv:2006.06127
21 D Kasprowski, P Lambert-Cole, M Land, A G Lecuona, Topologically flat embedded 2–spheres in specific simply connected 4–manifolds, from: "2019–20 MATRIX annals" (editors D R Wood, J de Gier, C E Praeger, T Tao), MATRIX Book Ser. 4, Springer (2021) 111 MR4294763
22 D Kasprowski, M Powell, P Teichner, The Kervaire–Milnor invariant in the stable classification of spin 4–manifolds, preprint (2021) arXiv:2105.12153
23 M H Kim, P Orson, J Park, A Ray, Good groups, from: "The disc embedding theorem" (editors S Behrens, B Kalmár, M H Kim, M Powell, A Ray), Oxford Univ. Press (2021) 273 MR4519517
24 R C Kirby, L R Taylor, A survey of 4–manifolds through the eyes of surgery, from: "Surveys on surgery theory, II" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 387 MR1818779
25 V S Krushkal, F Quinn, Subexponential groups in 4–manifold topology, Geom. Topol. 4 (2000) 407 MR1796498
26 R Lee, D M Wilczyński, Locally flat 2–spheres in simply connected 4–manifolds, Comment. Math. Helv. 65 (1990) 388 MR1069816
27 R Lee, D M Wilczyński, Representing homology classes by locally flat surfaces of minimum genus, Amer. J. Math. 119 (1997) 1119 MR1473071
28 P Lisca, G Matić, Stein 4–manifolds with boundary and contact structures, Topology Appl. 88 (1998) 55 MR1634563
29 C Manolescu, M Marengon, L Piccirillo, Relative genus bounds in indefinite four-manifolds, Math. Ann. (2024)
30 M Marengon, A N Miller, A Ray, A I Stipsicz, A note on surfaces in ℂℙ2 and ℂℙ2 # ℂℙ2, Proc. Amer. Math. Soc. Ser. B 11 (2024) 187
31 W S Massey, Proof of a conjecture of Whitney, Pacific J. Math. 31 (1969) 143 MR0250331
32 Y Matsumoto, Secondary intersectional properties of 4–manifolds and Whitney’s trick, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 99 MR0520526
33 Y Matsumoto, An elementary proof of Rochlin’s signature theorem and its extension by Guillou and Marin, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 119 MR0900248
34 R A Norman, Dehn’s lemma for certain 4–manifolds, Invent. Math. 7 (1969) 143 MR246309
35 J Pichelmeyer, Genera of knots in the complex projective plane, J. Knot Theory Ramifications 29 (2020) 2050081 MR4193876
36 M Powell, A Ray, Basic geometric constructions, from: "The disc embedding theorem" (editors S Behrens, B Kalmár, M H Kim, M Powell, A Ray), Oxford Univ. Press (2021) 217 MR4519513
37 M Powell, A Ray, Intersection numbers and the statement of the disc embedding theorem, from: "The disc embedding theorem" (editors S Behrens, B Kalmár, M H Kim, M Powell, A Ray), Oxford Univ. Press (2021) 155 MR4519509
38 M Powell, A Ray, P Teichner, The 4–dimensional disc embedding theorem and dual spheres, preprint (2020) arXiv:2006.05209
39 F Quinn, Ends of maps, III : Dimensions 4 and 5, J. Differential Geom. 17 (1982) 503 MR0679069
40 V A Rokhlin, New results in the theory of four-dimensional manifolds, Doklady Akad. Nauk SSSR 84 (1952) 221 MR0052101
41 V A Rokhlin, Proof of Gudkov’s hypothesis, Funct. Anal. Appl. 6 (1972) 136
42 R Schneiderman, Algebraic linking numbers of knots in 3–manifolds, Algebr. Geom. Topol. 3 (2003) 921 MR2012959
43 R Stong, Existence of π1–negligible embeddings in 4–manifolds : a correction to Theorem 10.5 of FQ, Proc. Amer. Math. Soc. 120 (1994) 1309 MR1215031
44 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR0248854
45 O Y Viro, Positioning in codimension 2, and the boundary, Uspehi Mat. Nauk 30 (1975) 231 MR420641
46 C T C Wall, Surgery on compact manifolds, 1, Academic (1970) MR431216
47 A Yasuhara, (2,15)–torus knot is not slice in P2, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991) 353 MR1151354
48 A Yasuhara, On slice knots in the complex projective plane, Rev. Mat. Univ. Complut. Madrid 5 (1992) 255 MR1195083