The topology of the space of symplectic balls in $ {S}^{2}\times {S}^{2}$

Sílvia Anjos; François Lalonde

doi:10.1016/j.crma.2007.10.025

Differential Geometry/Differential Topology

The topology of the space of symplectic balls in

S^{2} \times S^{2}

Presented by: Michèle Vergne

Sílvia Anjos ¹; François Lalonde ²

¹ Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal
² Département de mathématiques et de statistique, Université de Montréal, C.P. 6128 succ. Centre–Ville, Montréal QC H3C 3J7, Canada

Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 639-642

Abstract (Original language)
Résumé

In this Note we compute the full homotopy type of the space of symplectic embeddings of the standard ball $B^{4} (c) \subset R^{4}$ with capacity $c = π r^{2}$ into the 4-dimensional rational symplectic manifold $M_{μ} = (S^{2} \times S^{2}, μ ω_{0} \oplus ω_{0})$ where μ belongs to the interval $(1, 2]$ and c is above the critical value $μ - 1$ .

Dans cette Note, nous calculons le type d'homotopie complet de l'espace des plongements symplectiques de la boule standard $B^{4} (c) \subset R^{4}$ de capacité $c = π r^{2}$ dans la 4-variété rationnelle $M_{μ} = (S^{2} \times S^{2}, μ ω_{0} \oplus ω_{0})$ où μ appartient à l'intervalle $(1, 2]$ et c est plus grand que la valeur critique $μ - 1$ .

Received: 2007-06-28
Accepted: 2007-10-06
Published online: 2007-11-19

DOI: 10.1016/j.crma.2007.10.025

Author's affiliations:

Sílvia Anjos ¹; François Lalonde ²

¹ Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Lisboa, Portugal
² Département de mathématiques et de statistique, Université de Montréal, C.P. 6128 succ. Centre–Ville, Montréal QC H3C 3J7, Canada

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     author = {S{\'\i}lvia Anjos and Fran\c{c}ois Lalonde},
     title = {The topology of the space of symplectic balls in $ {S}^{2}\times {S}^{2}$},
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     pages = {639--642},
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     language = {en},
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Sílvia Anjos; François Lalonde. The topology of the space of symplectic balls in $ {S}^{2}\times {S}^{2}$. Comptes Rendus. Mathématique, Volume 345 (2007) no. 11, pp. 639-642. doi: 10.1016/j.crma.2007.10.025

References
Cited by

[1] S. Anjos; G. Granja Homotopy decomposition of a group of symplectomorphisms of $S^{2} \times S^{2}$ , Topology, Volume 43 (2004), pp. 599-618

[2] S. Anjos; F. Lalonde The homotopy type of the space of symplectic balls in $S^{2} \times S^{2}$ above the critical value | arXiv

[3] S. Anjos, F. Lalonde, M. Pinsonnault, in preparation

[4] F. Lalonde; M. Pinsonnault Groupes d'automorphismes et plongements symplectiques de boules dans les variétés rationelles, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 931-934

[5] F. Lalonde; M. Pinsonnault The topology of the space of symplectic balls in rational 4-manifolds, Duke Math. J., Volume 122 (2004) no. 2, pp. 347-397

[6] M. Pinsonnault, Symplectomorphism groups and embeddings of balls into rational ruled surfaces, Compositio Math., in press

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