Volume 10, issue 3 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Obstructions to special Lagrangian desingularizations and the Lagrangian prescribed boundary problem

Mark Haskins and Tommaso Pacini

Geometry & Topology 10 (2006) 1453–1521
Bibliography
1 V I Arnold, Lagrange and Legendre cobordisms I, Funktsional. Anal. i Prilozhen. 14 (1980) 1, 96 MR583797
2 D Auckly, L Kapitanski, Holonomy and Skyrme's model, Comm. Math. Phys. 240 (2003) 97 MR2004981
3 M Audin, Quelques calculs en cobordisme lagrangien, Ann. Inst. Fourier (Grenoble) 35 (1985) 159 MR810672
4 M Audin, Cobordismes d'immersions lagrangiennes et legendriennes, Travaux en Cours 20, Hermann (1987) MR903652
5 M Audin, J Lafontaine, editors, Holomorphic curves in symplectic geometry, Progress in Mathematics 117, Birkhäuser Verlag (1994) MR1274923
6 R Bott, L W Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer (1982) MR658304
7 G E Bredon, Topology and geometry, Graduate Texts in Mathematics 139, Springer (1993) MR1224675
8 A Butscher, Regularizing a singular special Lagrangian variety, Comm. Anal. Geom. 12 (2004) 733 MR2104075
9 E Carberry, I McIntosh, Minimal Lagrangian 2–tori in $\mathbb C\mathbb P^2$ come in real families of every dimension, J. London Math. Soc. $(2)$ 69 (2004) 531 MR2040620
10 I Castro, F Urbano, On a new construction of special Lagrangian immersions in complex Euclidean space, Q. J. Math. 55 (2004) 253 MR2082092
11 B N Cheng, Area-minimizing cone-type surfaces and coflat calibrations, Indiana Univ. Math. J. 37 (1988) 505 MR962922
12 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1990) MR1079726
13 Y Eliashberg, N Mishachev, Introduction to the $h$–principle, Graduate Studies in Mathematics 48, American Mathematical Society (2002) MR1909245
14 L Fu, On the boundaries of special Lagrangian submanifolds, Duke Math. J. 79 (1995) 405 MR1344766
15 H Geiges, Contact geometry, from: "Handbook of differential geometry. Vol. II", Elsevier/North-Holland, Amsterdam (2006) 315 MR2194671
16 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
17 M Gromov, Partial differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Springer (1986) MR864505
18 M Gross, Special Lagrangian fibrations I: Topology, from: "Integrable systems and algebraic geometry (Kobe/Kyoto, 1997)", World Sci. Publ., River Edge, NJ (1998) 156 MR1672120
19 M Gross, Special Lagrangian fibrations II: Geometry. A survey of techniques in the study of special Lagrangian fibrations, from: "Surveys in differential geometry: differential geometry inspired by string theory", Surv. Differ. Geom. 5, Int. Press, Boston (1999) 341 MR1772274
20 M Gross, Examples of special Lagrangian fibrations, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)", World Sci. Publ., River Edge, NJ (2001) 81 MR1882328
21 R Hardt, L Simon, Area minimizing hypersurfaces with isolated singularities, J. Reine Angew. Math. 362 (1985) 102 MR809969
22 R Harvey, H B Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47 MR666108
23 M Haskins, The geometric complexity of special Lagrangian $T^ 2$-cones, Invent. Math. 157 (2004) 11 MR2135184
24 M Haskins, Special Lagrangian cones, Amer. J. Math. 126 (2004) 845 MR2075484
25 M Haskins, N Kapouleas, Special Lagrangian cones with higher genus links, to appear in Inventiones Mathematicae arXiv:math.DG/0512178
26 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
27 M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242 MR0119214
28 D Joyce, Singularities of special Lagrangian fibrations and the SYZ conjecture, Comm. Anal. Geom. 11 (2003) 859 MR2032503
29 D Joyce, Special Lagrangian submanifolds with isolated conical singularities V: Survey and applications, J. Differential Geom. 63 (2003) 279 MR2015549
30 D Joyce, Singularities of special Lagrangian submanifolds, from: "Different faces of geometry", Int. Math. Ser. (N. Y.) 3, Kluwer/Plenum, New York (2004) 163 MR2102996
31 D Joyce, Special Lagrangian submanifolds with isolated conical singularities I: Regularity, Ann. Global Anal. Geom. 25 (2004) 201 MR2053761
32 D Joyce, Special Lagrangian submanifolds with isolated conical singularities II: Moduli spaces, Ann. Global Anal. Geom. 25 (2004) 301 MR2054572
33 D Joyce, Special Lagrangian submanifolds with isolated conical singularities III: Desingularization, the unobstructed case, Ann. Global Anal. Geom. 26 (2004) 1 MR2054578
34 D Joyce, Special Lagrangian submanifolds with isolated conical singularities IV: Desingularization, obstructions and families, Ann. Global Anal. Geom. 26 (2004) 117 MR2070685
35 A A Kosinski, Differential manifolds, Pure and Applied Mathematics 138, Academic Press (1993) MR1190010
36 D A Lee, Connected sums of special Lagrangian submanifolds, Comm. Anal. Geom. 12 (2004) 553 MR2128603
37 Y I Lee, Embedded special Lagrangian submanifolds in Calabi–Yau manifolds, Comm. Anal. Geom. 11 (2003) 391 MR2015752
38 J A Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976) 217 MR0410764
39 I McIntosh, Special Lagrangian cones in $\mathbb C^3$ and primitive harmonic maps, J. London Math. Soc. $(2)$ 67 (2003) 769 MR1967705
40 J W Milnor, A procedure for killing homotopy groups of differentiable manifolds., from: "Proc. Sympos. Pure Math., Vol. III", American Mathematical Society (1961) 39 MR0130696
41 J W Milnor, J D Stasheff, Characteristic classes, Annals of Mathematics Studies 76, Princeton University Press (1974) MR0440554
42 H Naitoh, Totally real parallel submanifolds in $P^{n}(c)$, Tokyo J. Math. 4 (1981) 279 MR646040
43 Y Ohnita, Stability and rigidity of special Lagrangian cones over certain minimal Legendrian orbits, to appear in Osaka J Math (2006)
44 L Polterovich, The surgery of Lagrange submanifolds, Geom. Funct. Anal. 1 (1991) 198 MR1097259
45 R Schoen, J Wolfson, The volume functional for Lagrangian submanifolds, from: "Lectures on partial differential equations", New Stud. Adv. Math. 2, Int. Press, Somerville, MA (2003) 181 MR2055848
46 S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. $(2)$ 69 (1959) 327 MR0105117
47 N Steenrod, The topology of fibre bundles, Princeton Landmarks in Mathematics, Princeton University Press (1999) MR1688579
48 A Strominger, S T Yau, E Zaslow, Mirror symmetry is $T$–duality, Nuclear Phys. B 479 (1996) 243 MR1429831
49 R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823
50 C T C Wall, Determination of the cobordism ring, Ann. of Math. $(2)$ 72 (1960) 292 MR0120654
51 J H C Whitehead, On $C^1$–complexes, Ann. of Math. $(2)$ 41 (1940) 809 MR0002545
52 H Whitney, The self-intersections of a smooth $n$–manifold in $2n$–space, Ann. of Math. $(2)$ 45 (1944) 220 MR0010274