Algebraic & Geometric Topology Volume 21, issue 5 (2021)

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No homotopy $4$–sphere invariants using $\mathrm{ECH} = \mathrm{SWF}$

Chris Gerig

Algebraic & Geometric Topology 21 (2021) 2543–2569

DOI: 10.2140/agt.2021.21.2543

Bibliography

1	J J Andrews, M L Curtis, Free groups and handlebodies, Proc. Amer. Math. Soc. 16 (1965) 192 MR173241
2	S Bauer, A stable cohomotopy refinement of Seiberg–Witten invariants, II, Invent. Math. 155 (2004) 21 MR2025299
3	F Bourgeois, K Niederkrüger, Towards a good definition of algebraically overtwisted, Expo. Math. 28 (2010) 85 MR2606237
4	J Cerf, Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1961) 227 MR140120
5	J Cerf, Sur les difféomorphismes de la sphère de dimension trois (Γ₄ = 0), 53, Springer (1968) MR0229250
6	Y Eliashberg, On symplectic manifolds with some contact properties, J. Differential Geom. 33 (1991) 233 MR1085141
7	Y Eliashberg, Contact 3–manifolds twenty years since J Martinet’s work, Ann. Inst. Fourier (Grenoble) 42 (1992) 165 MR1162559
8	Y Eliashberg, Symplectic topology in the nineties, Differential Geom. Appl. 9 (1998) 59 MR1636301
9	Y Eliashberg, N Mishachev, Introduction to the h–principle, 48, Amer. Math. Soc. (2002) MR1909245
10	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
11	H Geiges, K Zehmisch, Eliashberg’s proof of Cerf’s theorem, J. Topol. Anal. 2 (2010) 543 MR2748217
12	C Gerig, Seiberg–Witten and Gromov invariants for self-dual harmonic 2–forms, preprint (2018) arXiv:1809.03405
13	C Gerig, Taming the pseudoholomorphic beasts in ℝ × (S¹ × S²), Geom. Topol. 24 (2020) 1791 MR4173922
14	R E Gompf, Group actions, corks and exotic smoothings of ℝ⁴, Invent. Math. 214 (2018) 1131 MR3878728
15	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
16	K Honda, Transversality theorems for harmonic forms, Rocky Mountain J. Math. 34 (2004) 629 MR2072799
17	M Hutchings, The embedded contact homology index revisited, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lect. Notes 49, Amer. Math. Soc. (2009) 263 MR2555941
18	M Hutchings, Lecture notes on embedded contact homology, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 389 MR3220947
19	M Hutchings, C H Taubes, Proof of the Arnold chord conjecture in three dimensions, II, Geom. Topol. 17 (2013) 2601 MR3190296
20	P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209 MR1474156
21	P Kronheimer, T Mrowka, Monopoles and three-manifolds, 10, Cambridge Univ. Press (2007) MR2388043
22	P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. 165 (2007) 457 MR2299739
23	R Lockhart, Fredholm, Hodge and Liouville theorems on noncompact manifolds, Trans. Amer. Math. Soc. 301 (1987) 1 MR879560
24	K Luttinger, C Simpson, A normal form for the birth/flight of closed selfdual 2–form degeneracies, unpublished manuscript (1996)
25	D McDuff, Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991) 651 MR1091622
26	T Mrowka, Y Rollin, Legendrian knots and monopoles, Algebr. Geom. Topol. 6 (2006) 1 MR2199446
27	R S Palais, Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959) 125 MR116352
28	T Perutz, Zero-sets of near-symplectic forms, J. Symplectic Geom. 4 (2006) 237 MR2314214
29	D Salamon, Removable singularities and a vanishing theorem for Seiberg–Witten invariants, Turkish J. Math. 20 (1996) 61 MR1392663
30	R H Scott III, Closed self-dual two-forms on four-dimensional handlebodies, PhD thesis, Harvard University (2002)
31	C H Taubes, The geometry of the Seiberg–Witten invariants, from: "Surveys in differential geometry, III" (editor S T Yau), International (1998) 299 MR1677891
32	C H Taubes, The geometry of the Seiberg–Witten invariants, from: "Proceedings of the International Congress of Mathematicians, II" (editors G Fischer, U Rehmann), Deutsche Math. Vereinigung (1998) 493 MR1648099
33	C H Taubes, A proof of a theorem of Luttinger and Simpson about the number of vanishing circles of a near-symplectic form on a 4–dimensional manifold, Math. Res. Lett. 13 (2006) 557 MR2250491
34	C Taubes, A cancellation lemma and other dreams about almost symplectic forms, Broken Dreams seminar (2009)
35	C H Taubes, The Seiberg–Witten equations and the Weinstein conjecture, II : More closed integral curves of the Reeb vector field, Geom. Topol. 13 (2009) 1337 MR2496048
36	C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology, I, Geom. Topol. 14 (2010) 2497 MR2746723
37	S Vidussi, Seiberg–Witten invariants for manifolds diffeomorphic outside a circle, Proc. Amer. Math. Soc. 129 (2001) 2489 MR1823936
38	M L Yau, Vanishing of the contact homology of overtwisted contact 3–manifolds, Bull. Inst. Math. Acad. Sin. 1 (2006) 211 MR2230587
39	B Zhang, Monopoles and foliations without holonomy-invariant transverse measure, preprint (2021) arXiv:1603.08136v3