Lagrangian submanifolds and Lefschetz pencils.
| dc.contributor.author | Auroux, Denis | |
| dc.contributor.author | Muñoz, Vicente | |
| dc.contributor.author | Presas, Francisco | |
| dc.date.accessioned | 2023-06-20T10:34:35Z | |
| dc.date.available | 2023-06-20T10:34:35Z | |
| dc.date.issued | 2005 | |
| dc.description.abstract | Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction,we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | NSF | |
| dc.description.sponsorship | CICYT | |
| dc.description.sponsorship | CICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21115 | |
| dc.identifier.issn | 1527-5256 | |
| dc.identifier.officialurl | http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.jsg/1144947795 | |
| dc.identifier.relatedurl | http://projecteuclid.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50612 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Symplectic Geometry | |
| dc.language.iso | eng | |
| dc.page.final | 219 | |
| dc.page.initial | 171 | |
| dc.publisher | International Press | |
| dc.relation.projectID | DMS-0244844. | |
| dc.relation.projectID | BFM2000–0024 | |
| dc.relation.projectID | BFM2000–0024 | |
| dc.relation.projectID | HPRN-CT-2000-00101. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514 | |
| dc.subject.keyword | Symplectic | |
| dc.subject.keyword | Lefschetz pencil | |
| dc.subject.keyword | Lagrangian submanifold | |
| dc.subject.ucm | Geometría | |
| dc.subject.unesco | 1204 Geometría | |
| dc.title | Lagrangian submanifolds and Lefschetz pencils. | |
| dc.type | journal article | |
| dc.volume.number | 3 | |
| dcterms.references | J. Amoros, V. Muñoz and F. Presas, Generic behavior of asymptotically holomorphic pencils, J. Symplectic Geom. 2 (2004) 377–392 . D. Auroux, Asymptotically holomorphic families of symplectic submanifolds, Geom.Funct. Anal. 7 (1997), 971–995. D. Auroux, Symplectic 4-manifolds as branched coverings of CP2, Invent. Math. 139 (2000), 551–602. D. Auroux, Symplectic maps to projective spaces and symplectic invariants, Turkish J. Math. 25 (2001), 1–42. D. Auroux, Estimated transversality in symplectic geometry and projective maps,Symplectic Geometry and Mirror Symmetry (Seoul, 2000), 1–30, World Scientific,Singapore, 2001. D. Auroux, D. Gayet and J. P. Mohsen, Symplectic hypersurfaces in the complement of an isotropic submanifold, Math. Ann. 321 (2001), 739–754. D. Auroux and L. Katzarkov, A degree doubling formula for braid monodromies and Lefschetz pencils, preprint. J. Cerf, Sur les diffeomorphismes de la sphere de dimension trois (Γ4 = 0), Lecture Notes in Math. 53, Springer, 1968. S. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996), 666–705. S. Donaldson, Lefschetz pencils on symplectic manifolds, J. Differential Geom. 53 (1999), 205–236. R. Gompf, Toward a topological characterization of symplectic manifolds, J. Symplectic Geom. 2 (2004), 177–206. J. Milnor, Morse theory, Annals of Mathematics Studies, 51, Princeton University Press, Princeton, N.J., 1963. P. Seidel, Vanishing cycles and mutation, in Proceedings of 3rd European Congress of Mathematics (Barcelona, 2000),Vol. II, 65–85, Progr. Math. 202, Birkhauser, Basel,2001. P. Seidel, Lectures on four-dimensional Dehn twists,preprint math.SG/0309012. S. Smale, On the structure of manifolds, Amer. J. Math. 84 (1962), 387–399. I. Smith, Lefschetz pencils and divisors in moduli space, Geom. Topol. 5 (2001),579–608. M. Teicher, Braid groups, algebraic surfaces and fundamental groups of complements of branch curves, in ‘Algebraic Geometry’ (Santa Cruz, 1995), 127–150, Proc. Sympos.Pure Math., 62 (part 1), Amer. Math. Soc.,Providence, 1997. | |
| dspace.entity.type | Publication |
