Legendrian contact homology and generating families


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 Nazionalità Coordinatore France [FR]
 Totale costo 710˙000 €
 EC contributo 710˙000 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2009-StG
 Funding Scheme ERC-SG
 Anno di inizio 2009
 Periodo (anno-mese-giorno) 2009-11-01   -   2014-10-31


# participant  country  role  EC contrib. [€] 

 Organization address address: Avenue Franklin Roosevelt 50
postcode: 1050

contact info
Titolo: Dr.
Nome: Christine
Cognome: Courillon
Email: send email
Telefono: +32 2 650 67 18
Fax: +32 2 650 23 21

BE (BRUXELLES) beneficiary 486˙237.75

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Mr.
Nome: Nicolas
Cognome: Lecompte
Email: send email
Telefono: 33169155589

FR (ORSAY) hostInstitution 223˙762.25

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Prof.
Nome: Frédéric
Cognome: Bourgeois
Email: send email
Telefono: -6505810
Fax: -6505837

FR (ORSAY) hostInstitution 223˙762.25


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generating    theory    topology    holomorphic    dimensional    submanifolds    morse    recent    homology    structure    curves    manifold    contact    invariants    symplectic    linearized    existence    class    odd    legendrian   

 Obiettivo del progetto (Objective)

'A contact structure on an odd dimensional manifold in a maximally non integrable hyperplane field. It is the odd dimensional counterpart of a symplectic structure. Contact and symplectic topology is a recent and very active area that studies intrinsic questions about existence, (non) uniqueness and rigidity of contact and symplectic structures. It is intimately related to many other important disciplines, such as dynamical systems, singularity theory, knot theory, Morse theory, complex analysis, ... Legendrian submanifolds are a distinguished class of submanifolds in a contact manifold, which are tangent to the contact distribution. These manifolds are of a particular interest in contact topology. Important classes of Legendrian submanifolds can be described using generating families, and this description can be used to define Legendrian invariants via Morse theory. Other the other hand, Legendrian contact homology is an invariant for Legendrian submanifolds, based on holomorphic curves. The goal of this research proposal is to study the relationship between these two approaches. More precisely, we plan to show that the generating family homology and the linearized Legendrian contact homology can be defined for the same class of Legendrian submanifolds, and are isomorphic. This correspondence should be established using a parametrized version of symplectic homology, being developed by the Principal Investigator in collaboration with Oancea. Such a result would give an entirely new type of information about holomorphic curves invariants. Moreover, it can be used to obtain more general structural results on linearized Legendrian contact homology, to extend recent results on existence of Reeb chords, and to gain a much better understanding of the geography of Legendrian submanifolds.'

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