[Géométrie approximativement holomorphe et transversalité quantitative pour les variétés 2-calibrées]
On définit la notion de structure 2-calibrée, qui généralise celle de structure de contact, feuilletage tendu différentiable, etc. La géométrie approximativement holomorphe, introduite par S. Donaldson pour les variétés symplectiques est généralisée pour les variétés 2-calibrées. On démontre aussi un résultat de transversalité quantitative qui permet d'étudier la géométrie de ces variétés.
The notion of 2-calibrated structure, generalizing contact structures, smooth taut foliations, etc., is defined. Approximately holomorphic geometry as introduced by S. Donaldson for symplectic manifolds is extended to 2-calibrated manifolds. An estimated transversality result that enables to study the geometry of such manifolds is presented.
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@article{CRMATH_2004__338_9_709_0,
author = {Alberto Ibort and David Mart{\'\i}nez Torres},
title = {Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {709--712},
publisher = {Elsevier},
volume = {338},
number = {9},
year = {2004},
doi = {10.1016/j.crma.2004.03.003},
language = {en},
}
TY - JOUR AU - Alberto Ibort AU - David Martínez Torres TI - Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds JO - Comptes Rendus. Mathématique PY - 2004 SP - 709 EP - 712 VL - 338 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2004.03.003 LA - en ID - CRMATH_2004__338_9_709_0 ER -
Alberto Ibort; David Martínez Torres. Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 709-712. doi : 10.1016/j.crma.2004.03.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.003/
[1] Symplectic 4-manifolds as branched coverings of , Invent. Math., Volume 139 (2000), pp. 551-602
[2] Estimated transversality in symplectic geometry and projective maps, Symplectic Geometry and Mirror Symmetry (Seoul, 2000), World Sci. Publishing, River Edge, NJ, 2001, pp. 1-30
[3] B. Deroin, Laminations par variétés complexes, Thèse, École normale supérieure de Lyon, 2003
[4] Symplectic submanifolds and almost-complex geometry, J. Differential Geom., Volume 44 (1996), pp. 666-705
[5] Lefschetz fibrations in symplectic geometry, J. Differential Geom., Volume 53 (1999) no. 2, pp. 205-236
[6] Laminations par surfaces de Riemann, Dynamique et géométrie complexes (Lyon, 1997), ix, xi, Panor. Synthèses, vol. 8, Soc. Math. France, Paris, 1999, pp. 49-95
[7] Géométrie de contact : de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians, vol. II, Beijing, 2002, pp. 405-414
[8] Topological invariants of dynamical systems and spaces of holomorphic maps, I, Math. Phys. Anal. Geom., Volume 2 (1999) no. 4, pp. 323-415
[9] A. Ibort, D. Martínez Torres, in preparation
[10] On the construction of contact submanifolds with prescribed topology, J. Differential Geom., Volume 56 (2000) no. 2, pp. 235-283
[11] D. Martínez Torres, Geometries with topological character, Ph.D. Thesis, Universidad Carlos III de Madrid, 2003
[12] J.P. Mohsen, Transversalité quantitative et sous-variétés isotropes, Ph.D. Thesis, École Norm. Sup. Lyon, 2001
[13] Almost holomorphic embeddings in Grassmannians with applications to singular symplectic submanifolds, J. Reine Angew. Math., Volume 547 (2002), pp. 149-189
[14] Kähler identity on Levi flat manifolds and application to the embedding, Nagoya Math. J., Volume 158 (2000), pp. 87-93
[15] Lefschetz type pencils on contact manifolds, Asian J. Math., Volume 6 (2002) no. 2, pp. 277-301
[16] Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., Volume 36 (1976), pp. 225-255
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Commentaires - Politique
Lefschetz pencil structures for 2-calibrated manifolds
Alberto Ibort; David Marti´nez Torres
C. R. Math (2004)