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Topologically isotopic and smoothly inequivalent $2$–spheres in simply connected $4$–manifolds whose complement has a prescribed fundamental group

Rafael Torres

Algebraic & Geometric Topology 24 (2024) 2351–2365
Bibliography
1 S Akbulut, Scharlemann’s manifold is standard, Ann. of Math. 149 (1999) 497 MR1689337
2 S Akbulut, Isotoping 2–spheres in 4–manifolds, from: "Proceedings of the Gökova Geometry/Topology Conference 2014" (editors S Akbulut, D Auroux, T Önder), GGT (2015) 264 MR3381446
3 S Akbulut, 4–manifolds, 25, Oxford Univ. Press (2016) MR3559604
4 A Akhmedov, B D Park, Exotic smooth structures on small 4–manifolds with odd signatures, Invent. Math. 181 (2010) 577 MR2660453
5 A Akhmedov, R . Baykur, B D Park, Constructing infinitely many smooth structures on small 4–manifolds, J. Topol. 1 (2008) 409 MR2399137
6 D Auckly, H J Kim, P Melvin, D Ruberman, Stable isotopy in four dimensions, J. Lond. Math. Soc. 91 (2015) 439 MR3355110
7 S Baldridge, P Kirk, Constructions of small symplectic 4–manifolds using Luttinger surgery, J. Differential Geom. 82 (2009) 317 MR2520795
8 R . Baykur, N Sunukjian, Round handles, logarithmic transforms and smooth 4–manifolds, J. Topol. 6 (2013) 49 MR3029421
9 R Fintushel, R J Stern, Pinwheels and nullhomologous surgery on 4–manifolds with b+ = 1, Algebr. Geom. Topol. 11 (2011) 1649 MR2821436
10 R Fintushel, R Stern, Surgery on nullhomologous tori, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18, Geom. Topol. Publ. (2012) 61 MR3084232
11 R Fintushel, B D Park, R J Stern, Reverse engineering small 4–manifolds, Algebr. Geom. Topol. 7 (2007) 2103 MR2366188
12 M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
13 R E Gompf, Sums of elliptic surfaces, J. Differential Geom. 34 (1991) 93 MR1114454
14 R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
15 I Hambleton, M Kreck, Cancellation, elliptic surfaces and the topology of certain four-manifolds, J. Reine Angew. Math. 444 (1993) 79 MR1241794
16 I Hambleton, M Kreck, Cancellation of hyperbolic forms and topological four-manifolds, J. Reine Angew. Math. 443 (1993) 21 MR1241127
17 H J Kim, Modifying surfaces in 4–manifolds by twist spinning, Geom. Topol. 10 (2006) 27 MR2207789
18 H J Kim, D Ruberman, Smooth surfaces with non-simply-connected complements, Algebr. Geom. Topol. 8 (2008) 2263 MR2465741
19 D Kotschick, J W Morgan, C H Taubes, Four-manifolds without symplectic structures but with nontrivial Seiberg–Witten invariants, Math. Res. Lett. 2 (1995) 119 MR1324695
20 R Lee, D M Wilczyński, Locally flat 2–spheres in simply connected 4–manifolds, Comment. Math. Helv. 65 (1990) 388 MR1069816
21 R Lee, D M Wilczyński, Representing homology classes by locally flat surfaces of minimum genus, Amer. J. Math. 119 (1997) 1119 MR1473071
22 B Moishezon, Complex surfaces and connected sums of complex projective planes, 603, Springer (1977) MR0491730
23 J W Morgan, T S Mrowka, Z Szabó, Product formulas along T3 for Seiberg–Witten invariants, Math. Res. Lett. 4 (1997) 915 MR1492130
24 S P Plotnick, Equivariant intersection forms, knots in S4, and rotations in 2–spheres, Trans. Amer. Math. Soc. 296 (1986) 543 MR0846597
25 Y Sato, Locally flat 2–knots in S2 × S2 with the same fundamental group, Trans. Amer. Math. Soc. 323 (1991) 911 MR0986701
26 H R Schwartz, Equivalent non-isotopic spheres in 4–manifolds, J. Topol. 12 (2019) 1396 MR4138734
27 N S Sunukjian, Surfaces in 4–manifolds : concordance, isotopy, and surgery, Int. Math. Res. Not. 2015 (2015) 7950 MR3404006
28 M Tange, The link surgery of S2 × S2 and Scharlemann’s manifolds, Hiroshima Math. J. 44 (2014) 35 MR3178435
29 C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809 MR1306023