Geometry & Topology Volume 23, issue 5 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Geometrically simply connected $4$–manifolds and stable cohomotopy Seiberg–Witten invariants

Kouichi Yasui

Geometry & Topology 23 (2019) 2685–2697

DOI: 10.2140/gt.2019.23.2685

Bibliography

1	S Akbulut, The Dolgachev surface : disproving the Harer–Kas–Kirby conjecture, Comment. Math. Helv. 87 (2012) 187 MR2874900
2	S Akbulut, R Kirby, Branched covers of surfaces in 4–manifolds, Math. Ann. 252 (1979/80) 111 MR593626
3	A Akhmedov, M Ishida, B D Park, Reducible smooth structures on 4–manifolds with zero signature, J. Topol. 7 (2014) 607 MR3252957
4	S Bauer, A stable cohomotopy refinement of Seiberg–Witten invariants, II, Invent. Math. 155 (2004) 21 MR2025299
5	S Bauer, Refined Seiberg–Witten invariants, from: "Different faces of geometry" (editors S Donaldson, Y Eliashberg, M Gromov), Int. Math. Ser. (NY) 3, Kluwer (2004) 1 MR2102993
6	S Bauer, M Furuta, A stable cohomotopy refinement of Seiberg–Witten invariants, I, Invent. Math. 155 (2004) 1 MR2025298
7	R İ Baykur, M Ishida, Families of 4–manifolds with nontrivial stable cohomotopy Seiberg–Witten invariants, and normalized Ricci flow, J. Geom. Anal. 24 (2014) 1716 MR3261715
8	A Beauville, Surfaces complexes et orientation, from: "Geometry of K3 surfaces : moduli and periods", Astérisque 126, Soc. Mat. de France (1985) 41 MR785221
9	R Fintushel, R J Stern, Immersed spheres in 4–manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995) 145 MR1349567
10	R Fintushel, R J Stern, Knots, links, and 4–manifolds, Invent. Math. 134 (1998) 363 MR1650308
11	K A Frøyshov, Monopoles over 4–manifolds containing long necks, I, Geom. Topol. 9 (2005) 1 MR2115668
12	K A Frøyshov, Compactness and gluing theory for monopoles, 15, Geometry & Topology Publications (2008) MR2465077
13	R E Gompf, Nuclei of elliptic surfaces, Topology 30 (1991) 479 MR1113691
14	R E Gompf, A I Stipsicz, 4–Manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
15	J Harer, On handlebody structures for hypersurfaces in ℂ³ and ℂP³, Math. Ann. 238 (1978) 51 MR510306
16	J Harer, A Kas, R Kirby, Handlebody decompositions of complex surfaces, 350, Amer. Math. Soc. (1986) MR849942
17	J Hom, T Lidman, A note on positive-definite, symplectic four-manifolds, J. Eur. Math. Soc. 21 (2019) 257 MR3880209
18	M Ishida, C LeBrun, Curvature, connected sums, and Seiberg–Witten theory, Comm. Anal. Geom. 11 (2003) 809 MR2032500
19	M Ishida, H Sasahira, Stable cohomotopy Seiberg–Witten invariants of connected sums of four-manifolds with positive first Betti number, I : Non-vanishing theorem, Internat. J. Math. 26 (2015) MR3356875
20	M Ishida, H Sasahira, Stable cohomotopy Seiberg–Witten invariants of connected sums of four-manifolds with positive first Betti number, II : Applications, Comm. Anal. Geom. 25 (2017) 373 MR3690245
21	A Juhász, D P Thurston, I Zemke, Naturality and mapping class groups in Heegaard Floer homology, preprint (2012) arXiv:1210.4996
22	T Khandhawit, J Lin, H Sasahira, Unfolded Seiberg–Witten Floer spectra, II : Relative invariants and the gluing theorem, preprint (2018) arXiv:1809.09151
23	R Kirby, Problems in low dimensional manifold theory, II, from: "Algebraic and geometric topology" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 273 MR520548
24	D Kotschick, Orientation-reversing homeomorphisms in surface geography, Math. Ann. 292 (1992) 375 MR1149041
25	D Kotschick, Orientations and geometrisations of compact complex surfaces, Bull. London Math. Soc. 29 (1997) 145 MR1425990
26	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
27	P B Kronheimer, Minimal genus in S¹ × M³, Invent. Math. 135 (1999) 45 MR1664695
28	P B Kronheimer, T S Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994) 797 MR1306022
29	V T Liem, G A Venema, Representing homology classes of simply connected 4-manifolds, Topology Appl. 120 (2002) 57 MR1895483
30	R Mandelbaum, Special handlebody decompositions of simply connected algebraic surfaces, Proc. Amer. Math. Soc. 80 (1980) 359 MR577774
31	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
32	P Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006) 326 MR2222356
33	J Park, The geography of symplectic 4-manifolds with an arbitrary fundamental group, Proc. Amer. Math. Soc. 135 (2007) 2301 MR2299508
34	J Rasmussen, Perfect Morse functions and exotic S² × S²’s, preprint (2010) arXiv:1005.4674
35	H Sasahira, Spin structures on Seiberg–Witten moduli spaces, J. Math. Sci. Univ. Tokyo 13 (2006) 347 MR2284407
36	C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809 MR1306023
37	K Yasui, Exotic rational elliptic surfaces without 1–handles, Algebr. Geom. Topol. 8 (2008) 971 MR2443105
38	K Yasui, Elliptic surfaces without 1–handles, J. Topol. 1 (2008) 857 MR2461858
39	K Yasui, Small exotic rational surfaces without 1– and 3–handles, Trans. Amer. Math. Soc. 362 (2010) 5893 MR2661501
40	K Yasui, Stably exotic 4–manifolds, in preparation
41	I Zemke, Graph cobordisms and Heegaard Floer homology, preprint (2015) arXiv:1512.01184