Éclatement et contraction lagrangiens et applications
dc.contributor.advisor | Cornea, Octavian | |
dc.contributor.advisor | Lalonde, François | |
dc.contributor.author | Rieser, Antonio P. | |
dc.date.accessioned | 2011-01-21T17:03:44Z | |
dc.date.available | NO_RESTRICTION | en |
dc.date.available | 2011-01-21T17:03:44Z | |
dc.date.issued | 2010-12-02 | |
dc.date.submitted | 2010-08 | |
dc.identifier.uri | http://hdl.handle.net/1866/4532 | |
dc.subject | Symplectique | en |
dc.subject | Quatre-variétés | en |
dc.subject | Sous-variété lagrangienne | en |
dc.subject | Packing | en |
dc.subject | Packing relatif | en |
dc.subject | Involution anti-symplectique | en |
dc.subject | Variété réelle | en |
dc.subject | Real symplectic manifolds | en |
dc.subject | Relative packing | en |
dc.subject | Anti-symplectic involution | en |
dc.subject | Four-manifolds | en |
dc.subject | Symplectic | en |
dc.subject.other | Mathematics / Mathématiques (UMI : 0405) | en |
dc.title | Éclatement et contraction lagrangiens et applications | en |
dc.type | Thèse ou mémoire / Thesis or Dissertation | |
etd.degree.discipline | Mathématiques | en |
etd.degree.grantor | Université de Montréal | fr |
etd.degree.level | Doctorat / Doctoral | en |
etd.degree.name | Ph. D. | en |
dcterms.abstract | Soit (M, ω) une variété symplectique. Nous construisons une version de l’éclatement et de la contraction symplectique, que nous définissons relative à une sous-variété lagrangienne L ⊂ M. En outre, si M admet une involution anti-symplectique ϕ, et que nous éclatons une configuration suffisament symmetrique des plongements de boules, nous démontrons qu’il existe aussi une involution anti-symplectique sur l’éclatement ~M. Nous dérivons ensuite une condition homologique pour les surfaces lagrangiennes réeles L = Fix(ϕ), qui détermine quand la topologie de L change losqu’on contracte une courbe exceptionnelle C dans M. Finalement, on utilise ces constructions afin d’étudier le packing relatif dans (ℂP²,ℝP²). | en |
dcterms.abstract | Given a symplectic manifold (M,ω) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L. Furthermore, if M admits an anti-symplectic involution ϕ, i.e. a diffeomorphism such that ϕ2 = Id and ϕ*ω = —ω , and we blow-up an appropriately symmetric configuration of symplectic balls, then we show that there exists an antisymplectic involution on the blow-up ~M as well. We derive a homological condition for real Lagrangian surfaces L = Fix(ϕ) which determines when the topology of L changes after a blow down, and we then use these constructions to study the real packing numbers for real Lagrangian submanifolds in (ℂP²,ℝP²). | en |
dcterms.language | eng | en |
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