Geometry & Topology Volume 27, issue 5 (2023)

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

Isotopy of the Dehn twist on $K3\mathbin{\#} K3$ after a single stabilization

Jianfeng Lin

Geometry & Topology 27 (2023) 1987–2012

DOI: 10.2140/gt.2023.27.1987

Bibliography

1	J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR764596
2	S Akbulut, A fake 4–manifold, from: "Four-manifold theory" (editors C Gordon, R Kirby), Contemp. Math. 35, Amer. Math. Soc. (1984) 75 MR780576
3	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
4	S Akbulut, T Mrowka, Y Ruan, Torsion classes and a universal constraint on Donaldson invariants for odd manifolds, Trans. Amer. Math. Soc. 347 (1995) 63 MR1270658
5	D Auckly, H J Kim, P Melvin, D Ruberman, Stable isotopy in four dimensions, J. Lond. Math. Soc. 91 (2015) 439 MR3355110
6	D Auckly, H J Kim, P Melvin, D Ruberman, H Schwartz, Isotopy of surfaces in 4–manifolds after a single stabilization, Adv. Math. 341 (2019) 609 MR3873547
7	D Baraglia, Constraints on families of smooth 4–manifolds from Bauer–Furuta invariants, Algebr. Geom. Topol. 21 (2021) 317 MR4224743
8	D Baraglia, H Konno, A gluing formula for families Seiberg–Witten invariants, Geom. Topol. 24 (2020) 1381 MR4157556
9	D Baraglia, H Konno, On the Bauer–Furuta and Seiberg–Witten invariants of families of 4–manifolds, J. Topol. 15 (2022) 505 MR4441598
10	S Bauer, A stable cohomotopy refinement of Seiberg–Witten invariants, II, Invent. Math. 155 (2004) 21 MR2025299
11	S Bauer, M Furuta, A stable cohomotopy refinement of Seiberg–Witten invariants, I, Invent. Math. 155 (2004) 1 MR2025298
12	R İ Baykur, N Sunukjian, Round handles, logarithmic transforms and smooth 4–manifolds, J. Topol. 6 (2013) 49 MR3029421
13	S E Cappell, J L Shaneson, Some new four-manifolds, Ann. of Math. 104 (1976) 61 MR418125
14	T tom Dieck, Transformation groups and representation theory, 766, Springer (1979) MR551743
15	T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
16	S K Donaldson, Irrationality and the h–cobordism conjecture, J. Differential Geom. 26 (1987) 141 MR892034
17	S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397 MR910015
18	S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Univ. Press (1990) MR1079726
19	R Fintushel, R J Stern, 2–Torsion instanton invariants, J. Amer. Math. Soc. 6 (1993) 299 MR1168958
20	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
21	M Furuta, Monopole equation and the –conjecture, Math. Res. Lett. 8 (2001) 279 MR1839478
22	R E Gompf, Stable diffeomorphism of compact 4–manifolds, Topology Appl. 18 (1984) 115 MR769285
23	M Kreck, Isotopy classes of diffeomorphisms of (k−1)–connected almost-parallelizable 2k–manifolds, from: "Algebraic topology" (editors J L Dupont, I H Madsen), Lecture Notes in Math. 763, Springer (1979) 643 MR561244
24	M Kreck, Some closed 4–manifolds with exotic differentiable structure, from: "Algebraic topology" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 246 MR764582
25	M Kreck, Surgery and duality, Ann. of Math. 149 (1999) 707 MR1709301
26	P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU(2), Math. Res. Lett. 11 (2004) 741 MR2106239
27	N H Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965) 19 MR179792
28	L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
29	J Lin, A Mukherjee, Family Bauer–Furuta invariant, exotic surfaces and Smale conjecture, preprint (2021) arXiv:2110.09686
30	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
31	B Perron, Pseudo-isotopies et isotopies en dimension quatre dans la catégorie topologique, Topology 25 (1986) 381 MR862426
32	F Quinn, Isotopy of 4–manifolds, J. Differential Geom. 24 (1986) 343 MR868975
33	D Ruberman, An obstruction to smooth isotopy in dimension 4, Math. Res. Lett. 5 (1998) 743 MR1671187
34	S Schwede, Lectures on equivariant stable homotopy theory, preprint (2014)
35	M Szymik, Characteristic cohomotopy classes for families of 4–manifolds, Forum Math. 22 (2010) 509 MR2652709
36	C T C Wall, Diffeomorphisms of 4–manifolds, J. London Math. Soc. 39 (1964) 131 MR163323
37	C T C Wall, On simply-connected 4–manifolds, J. London Math. Soc. 39 (1964) 141 MR163324
38	M Xu, The Bauer–Furuta invariant and a cohomotopy refined Ruberman invariant, PhD thesis, Stony Brook University (2004) MR2706507