Geometry & Topology Volume 22, issue 5 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Exotic open $4$–manifolds which are nonleaves

Carlos Meniño Cotón and Paul A Schweitzer

Geometry & Topology 22 (2018) 2791–2816

DOI: 10.2140/gt.2018.22.2791

Bibliography

1	T Asselmeyer-Maluga, C H Brans, Exotic smoothness and physics: differential topology and spacetime models, World Sci. (2007) MR2298917
2	O Attie, S Hurder, Manifolds which cannot be leaves of foliations, Topology 35 (1996) 335 MR1380502
3	Ž Bižaca, J Etnyre, Smooth structures on collarable ends of 4–manifolds, Topology 37 (1998) 461 MR1604866
4	A Candel, L Conlon, Foliations, I, 23, Amer. Math. Soc. (2000) MR1732868
5	J Cantwell, L Conlon, Poincaré–Bendixson theory for leaves of codimension one, Trans. Amer. Math. Soc. 265 (1981) 181 MR607116
6	J Cantwell, L Conlon, Every surface is a leaf, Topology 26 (1987) 265 MR899049
7	S De Michelis, M H Freedman, Uncountably many exotic R⁴’s in standard 4–space, J. Differential Geom. 35 (1992) 219 MR1152230
8	P R Dippolito, Codimension one foliations of closed manifolds, Ann. of Math. 107 (1978) 403 MR0515731
9	S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
10	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
11	M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
12	M H Freedman, L R Taylor, A universal smoothing of four-space, J. Differential Geom. 24 (1986) 69 MR857376
13	M Furuta, Monopole equation and the –conjecture, Math. Res. Lett. 8 (2001) 279 MR1839478
14	S Ganzell, Ends of 4–manifolds, Topology Proc. 30 (2006) 223 MR2280669
15	L J Gerstein, Basic quadratic forms, 90, Amer. Math. Soc. (2008) MR2396246
16	É Ghys, Une variété qui n’est pas une feuille, Topology 24 (1985) 67 MR790676
17	R E Gompf, An infinite set of exotic R⁴’s, J. Differential Geom. 21 (1985) 283 MR816673
18	R E Gompf, An exotic menagerie, J. Differential Geom. 37 (1993) 199 MR1198606
19	R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
20	R E Greene, Complete metrics of bounded curvature on noncompact manifolds, Arch. Math. (Basel) 31 (1978) 89 MR510080
21	A Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa 16 (1962) 367 MR0189060
22	G Hector, Croissance des feuilletages presque sans holonomie, from: "Differential topology, foliations and Gelfand–Fuks cohomology" (editor P A Schweitzer), Lecture Notes in Math. 652, Springer (1978) 141 MR505659
23	T Inaba, T Nishimori, M Takamura, N Tsuchiya, Open manifolds which are nonrealizable as leaves, Kodai Math. J. 8 (1985) 112 MR776712
24	T Januszkiewicz, Characteristic invariants of noncompact Riemannian manifolds, Topology 23 (1984) 289 MR770565
25	J Król, Exotic smooth 4–manifolds and gerbes as geometry for quantum gravity, Acta Phys. Polon. B 40 (2009) 3079 MR2565870
26	J A Álvarez López, R Barral Lijó, Bounded geometry and leaves, Math. Nachr. 290 (2017) 1448 MR3672890
27	A Navas, Groups of circle diffeomorphisms, Univ. of Chicago Press (2011) MR2809110
28	A Phillips, D Sullivan, Geometry of leaves, Topology 20 (1981) 209 MR605659
29	F Quinn, Ends of maps, III : Dimensions 4 and 5, J. Differential Geom. 17 (1982) 503 MR679069
30	P A Schweitzer, Riemannian manifolds not quasi-isometric to leaves in codimension one foliations, Ann. Inst. Fourier (Grenoble) 61 (2011) 1599 MR2951506
31	J P Serre, A course in arithmetic, 7, Springer (1973) MR0344216
32	C H Taubes, Gauge theory on asymptotically periodic 4–manifolds, J. Differential Geom. 25 (1987) 363 MR882829
33	L R Taylor, An invariant of smooth 4–manifolds, Geom. Topol. 1 (1997) 71 MR1483766
34	L R Taylor, Impossible metric conditions on exotic ℝ⁴’s, Asian J. Math. 12 (2008) 285 MR2453556
35	H Whitney, Differentiable manifolds, Ann. of Math. 37 (1936) 645 MR1503303
36	A Zeghib, An example of a 2–dimensional no leaf, from: "Geometric study of foliations" (editors T Mizutani, K Masuda, S Matsumoto, T Inaba, T Tsuboi, Y Mitsumatsu), World Sci. (1994) 475 MR1363743