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A note on the complexity of $h$–cobordisms

Hannah R Schwartz

Algebraic & Geometric Topology 20 (2020) 3313–3327
Bibliography
1 S Akbulut, A fake compact contractible 4–manifold, J. Differential Geom. 33 (1991) 335 MR1094459
2 J Cerf, Sur les difféomorphismes de la sphère de dimension trois 4 = 0), 53, Springer (1968) MR0229250
3 C L Curtis, M H Freedman, W C Hsiang, R Stong, A decomposition theorem for h–cobordant smooth simply-connected compact 4–manifolds, Invent. Math. 123 (1996) 343 MR1374205
4 S K Donaldson, Irrationality and the h–cobordism conjecture, J. Differential Geom. 26 (1987) 141 MR892034
5 S K Donaldson, The Seiberg–Witten equations and 4–manifold topology, Bull. Amer. Math. Soc. 33 (1996) 45 MR1339810
6 R Fintushel, R J Stern, Immersed spheres in 4–manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995) 145 MR1349567
7 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
8 D Y Gan, J H Guo, Embeddings and immersions of a 2–sphere in 4–manifolds, Proc. Amer. Math. Soc. 118 (1993) 1323 MR1152976
9 H Z Gao, Representing homology classes of almost definite 4–manifolds, Topology Appl. 52 (1993) 109 MR1241187
10 H Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie (1952) MR0049239
11 M Kreck, h–cobordisms between 1–connected 4–manifolds, Geom. Topol. 5 (2001) 1 MR1812433
12 P B Kronheimer, T S Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994) 797 MR1306022
13 P B Kronheimer, T S Mrowka, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. 30 (1994) 215 MR1246469
14 K Kuga, Representing homology classes of S2 × S2, Topology 23 (1984) 133 MR744845
15 R K Lashof, S Smale, Self-intersections of immersed manifolds, J. Math. Mech. 8 (1959) 143 MR0101522
16 T Lawson, Representing homology classes of almost definite 4–manifolds, Michigan Math. J. 34 (1987) 85 MR873022
17 T Lawson, h–cobordisms between simply connected 4–manifolds, Topology Appl. 28 (1988) 75 MR927283
18 T Lawson, The minimal genus problem, Expo. Math. 15 (1997) 385 MR1486407
19 B H Li, Representing nonnegative homology classes of P2nP2 by minimal genus smooth embeddings, Trans. Amer. Math. Soc. 352 (2000) 4155 MR1637082
20 B H Li, T J Li, Minimal genus smooth embeddings in S2 × S2 and P2nP2 with n 8, Topology 37 (1998) 575 MR1604887
21 T J Li, A Liu, General wall crossing formula, Math. Res. Lett. 2 (1995) 797 MR1362971
22 R Matveyev, A decomposition of smooth simply-connected h–cobordant 4–manifolds, J. Differential Geom. 44 (1996) 571 MR1431006
23 J W Morgan, The Seiberg–Witten equations and applications to the topology of smooth four-manifolds, 44, Princeton Univ. Press (1996) MR1367507
24 J W Morgan, Z Szabó, On h–cobordisms and Seiberg–Witten invariants, from: "Topics in symplectic 4–manifolds" (editor R J Stern), First Int. Press Lect. Ser. 1, International (1998) 117 MR1635699
25 J W Morgan, Z Szabó, Complexity of 4–dimensional h–cobordisms, Invent. Math. 136 (1999) 273 MR1688374
26 J W Morgan, Z Szabó, C H Taubes, A product formula for the Seiberg–Witten invariants and the generalized Thom conjecture, J. Differential Geom. 44 (1996) 706 MR1438191
27 R A Norman, Dehn’s lemma for certain 4–manifolds, Invent. Math. 7 (1969) 143 MR246309
28 D Ruberman, The minimal genus of an embedded surface of non-negative square in a rational surface, Turkish J. Math. 20 (1996) 129 MR1392668
29 S Smale, On the structure of manifolds, Amer. J. Math. 84 (1962) 387 MR153022
30 J R Stallings, On infinite processes leading to differentiability in the complement of a point, from: "Differential and combinatorial topology" (editor S S Cairns), Princeton Univ. Press (1965) 245 MR0180983
31 S Strle, Bounds on genus and geometric intersections from cylindrical end moduli spaces, J. Differential Geom. 65 (2003) 469 MR2064429
32 A I Suciu, Immersed spheres in P2 and S2 × S2, Math. Z. 196 (1987) 51 MR907407
33 C T C Wall, On the orthogonal groups of unimodular quadratic forms, Math. Ann. 147 (1962) 328 MR138565
34 C T C Wall, Diffeomorphisms of 4–manifolds, J. Lond. Math. Soc. 39 (1964) 131 MR163323
35 C T C Wall, On simply-connected 4–manifolds, J. Lond. Math. Soc. 39 (1964) 141 MR163324
36 C T C Wall, On the orthogonal groups of unimodular quadratic forms, II, J. Reine Angew. Math. 213 (1964) 122 MR155798
37 H Whitney, The self-intersections of a smooth n–manifold in 2n–space, Ann. of Math. 45 (1944) 220 MR10274
38 X Zhao, H Gao, H Qiu, The minimal genus problem in rational surfaces P2nP2, Sci. China Ser. A 49 (2006) 1275 MR2284210