Higher type adjunction inequalities for Donaldson invariants.
| dc.contributor.author | Muñoz, Vicente | |
| dc.date.accessioned | 2023-06-20T18:43:56Z | |
| dc.date.available | 2023-06-20T18:43:56Z | |
| dc.date.issued | 2001 | |
| dc.description.abstract | We prove new adjunction inequalities for embedded surfaces in four-manifolds with non-negative self-intersection number using the Donaldson invariants. These formulas are completely analogous to the ones obtained by Ozsvath and Szabo using the Seiberg-Witten invariants. To prove these relations, we give a fairly explicit description of the structure of the Fukaya-Floer homology of a surface times a circle. As an aside, we also relate the Floer homology of a surface times a circle with the cohomology of some symmetric products of the surface. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21281 | |
| dc.identifier.doi | 10.2307/2118573 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/2001-353-07/S0002-9947-01-02793-3/S0002-9947-01-02793-3.pdf | |
| dc.identifier.relatedurl | http://www.ams.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58462 | |
| dc.issue.number | 7 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 2654 | |
| dc.page.initial | 2635 | |
| dc.publisher | American Mathematical Society | |
| dc.relation.projectID | PB97-1095 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | 4-manifolds | |
| dc.subject.keyword | Adjunction inequalities | |
| dc.subject.keyword | Donaldson invariants | |
| dc.subject.keyword | Fukaya-Floer homology | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Higher type adjunction inequalities for Donaldson invariants. | |
| dc.type | journal article | |
| dc.volume.number | 353 | |
| dcterms.references | A. Bertram and M. Thaddeus, On the quantum cohomology of a symmetric product of an algebraic curve, math.AG/9803026 S. Dostoglou and D. Salamon, Self-dual instantons and holomorphic curves, Annals of Math.,139 1994, 581-640. MR 95g:58050 R. Fintushel and R. J. Stern, The blow-up formula for Donaldson invariants, Annals of Math.143 1996, 529-546. MR 97i:57036 K. Fukaya, Instanton homology for oriented 3-manifolds, Adv. Studies in Pure Mathematics,Ed. Y. Matsumoto and S. Morita. P. B. Kronheimer and T. S. Mrowka, Embedded surfaces and the structure of Donaldson's polynomial invariants, J. Dff. Geom. 41 1995, 573-734. MR 96e:57019 I. G. MacDonald, Symmetric products of an algebraic curve, Topology, 1 1962, 319-343. MR27:1445 V. Muñoz, Gluing formulae for Donaldson invariants for connected sums along surfaces, Asian J. Math. 1 1997, 785-800. MR 99m:57027 V. Muñoz, Ring structure of the Floer cohomology of Σ x S1 , Topology, 38 1999, 517-528.MR 99m:57028 V. Muñoz, Fukaya-Floer homology of Σ x S1 and applications, to appear in J. Diff. Geom. V. Muñoz, Basic classes for four-manifolds not of simple type, Comm. Anal. Geom. 8 2000,653-670. CMP 2000:16 V. Muñoz and B-L. Wang, Seiberg-Witten-Floer homology of a surface times a circle,math.DG/9905050. P. Osvath and Z. Szabo, Higher type adjunction inequalities in Seiberg-Witten theory,math.DG/0005268. E. Witten, Monopoles and four-manifolds, Math. Research Letters, 1 1994, 769-796. MR 96d:57035 | |
| dspace.entity.type | Publication |
