Geometry & Topology Volume 25, issue 2 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Characteristic classes via $4$–dimensional gauge theory

Hokuto Konno

Geometry & Topology 25 (2021) 711–773

DOI: 10.2140/gt.2021.25.711

Bibliography

1	M Abouzaid, Family Floer cohomology and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Yie), Kyung Moon Sa (2014) 813 MR3728639
2	M Abouzaid, The family Floer functor is faithful, J. Eur. Math. Soc. 19 (2017) 2139 MR3656481
3	M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR397797
4	M F Atiyah, I M Singer, The index of elliptic operators, IV, Ann. of Math. 93 (1971) 119 MR279833
5	D Baraglia, Obstructions to smooth group actions on 4–manifolds from families Seiberg–Witten theory, Adv. Math. 354 (2019) MR3981995
6	D Baraglia, H Konno, A gluing formula for families Seiberg–Witten invariants, Geom. Topol. 24 (2020) 1381 MR4157556
7	S Bauer, M Furuta, A stable cohomotopy refinement of Seiberg–Witten invariants, I, Invent. Math. 155 (2004) 1 MR2025298
8	O Buşe, Relative family Gromov–Witten invariants and symplectomorphisms, Pacific J. Math. 218 (2005) 315 MR2218350
9	S K Donaldson, Yang–Mills invariants of four-manifolds, from: "Geometry of low-dimensional manifolds, I" (editors S K Donaldson, C B Thomas), Lond. Math. Soc. Lect. Note Ser. 150, Cambridge Univ. Press (1990) 5 MR1171888
10	S K Donaldson, The Seiberg–Witten equations and 4–manifold topology, Bull. Amer. Math. Soc. 33 (1996) 45 MR1339810
11	S K Donaldson, Floer homology groups in Yang–Mills theory, 147, Cambridge Univ. Press (2002) MR1883043
12	P M N Feehan, T G Leness, SO(3) monopoles, level-one Seiberg–Witten moduli spaces, and Witten’s conjecture in low degrees, Topology Appl. 124 (2002) 221 MR1936209
13	P M N Feehan, T G Leness, An SO(3)–monopole cobordism formula relating Donaldson and Seiberg–Witten invariants, 1226, Amer. Math. Soc. (2018) MR3897982
14	K Fukaya, Floer homology for families: a progress report, from: "Integrable systems, topology, and physics" (editors M Guest, R Miyaoka, Y Ohnita), Contemp. Math. 309, Amer. Math. Soc. (2002) 33 MR1953352
15	M Furuta, A remark on a fixed point of finite group action on S⁴, Topology 28 (1989) 35 MR991097
16	B Hanke, D Kotschick, J Wehrheim, Dissolving four-manifolds and positive scalar curvature, Math. Z. 245 (2003) 545 MR2021570
17	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
18	M A Kervaire, Relative characteristic classes, Amer. J. Math. 79 (1957) 517 MR90051
19	H Konno, Bounds on genus and configurations of embedded surfaces in 4–manifolds, J. Topol. 9 (2016) 1130 MR3620461
20	H Konno, A cohomological Seiberg–Witten invariant emerging from the adjunction inequality, preprint (2017) arXiv:1704.05859
21	H Konno, Positive scalar curvature and higher-dimensional families of Seiberg–Witten equations, J. Topol. 12 (2019) 1246 MR3977876
22	A Kriegl, P W Michor, The convenient setting of global analysis, 53, Amer. Math. Soc. (1997) MR1471480
23	P B Kronheimer, Some non-trivial families of symplectic structures, preprint (1997)
24	S Lang, Differential and Riemannian manifolds, 160, Springer (1995) MR1335233
25	H V Lê, K Ono, Parameterized Gromov–Witten invariants and topology of symplectomorphism groups, from: "Groups of diffeomorphisms" (editors R Penner, D Kotschick, T Tsuboi, N Kawazumi, T Kitano, Y Mitsumatsu), Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 51 MR2509705
26	T J Li, A K Liu, Family Seiberg–Witten invariants and wall crossing formulas, Comm. Anal. Geom. 9 (2001) 777 MR1868921
27	J P May, A concise course in algebraic topology, Univ. Chicago Press (1999) MR1702278
28	D McDuff, The symplectomorphism group of a blow up, Geom. Dedicata 132 (2008) 1 MR2396906
29	R B Melrose, The Atiyah–Patodi–Singer index theorem, 4, Peters (1993) MR1348401
30	E Y Miller, The homology of the mapping class group, J. Differential Geom. 24 (1986) 1 MR857372
31	S Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 551 MR914849
32	D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, II : Geometry" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
33	N Nakamura, The Seiberg–Witten equations for families and diffeomorphisms of 4–manifolds, Asian J. Math. 7 (2003) 133 MR2015245
34	N Nakamura, Smoothability of ℤ × ℤ–actions on 4–manifolds, Proc. Amer. Math. Soc. 138 (2010) 2973 MR2644908
35	T Nishinou, Some nontrivial homology classes on the space of symplectic forms, J. Math. Kyoto Univ. 42 (2002) 599 MR1967225
36	J Park, The geography of Spin symplectic 4–manifolds, Math. Z. 240 (2002) 405 MR1900318
37	F Quinn, Isotopy of 4–manifolds, J. Differential Geom. 24 (1986) 343 MR868975
38	Y Ruan, Virtual neighborhoods and the monopole equations, from: "Topics in symplectic 4–manifolds" (editor R J Stern), International (1998) 101 MR1635698
39	D Ruberman, An obstruction to smooth isotopy in dimension 4, Math. Res. Lett. 5 (1998) 743 MR1671187
40	D Ruberman, A polynomial invariant of diffeomorphisms of 4–manifolds, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2, Geom. Topol. (1999) 473 MR1734421
41	D Ruberman, Positive scalar curvature, diffeomorphisms and the Seiberg–Witten invariants, Geom. Topol. 5 (2001) 895 MR1874146
42	M Szymik, Characteristic cohomotopy classes for families of 4–manifolds, Forum Math. 22 (2010) 509 MR2652709
43	C T C Wall, On simply-connected 4–manifolds, J. Lond. Math. Soc. 39 (1964) 141 MR163324