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SS2 - Topologie et géométrie symplectiques / SS2 - Symplectic topology and geometry
Org: D. Auroux (MIT/X) et/and F. Lalonde (Montréal)
- FRÉDÉRIC BOURGEOIS, Université Libre de Bruxelles
Homotopy groups of the space of contact structures
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We show how the functorial properties of contact homology can be used
to detect nontrivial elements in the homotopy groups of the space of
contact structures. This technique will then be illustrated with
various examples.
- OCTAV CORNEA, Université de Montréal, CP 6128 Succ. Centre Ville,
Montréal, Québec H3C 3J7, Canada
Cluster homology and detection of pseudoholomorphic disks and
strips
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In this talk I will review shortly the construction of the cluster
homology of a Lagrangian submanifold and describe some applications to
the detection of pseudoholomorphic disks (this part of the talk is
based on joint work with Francois Lalonde). I will also indicate how
this construction is related to a previous one-introduced jointly
with Jean-Francois Barraud-which serves to detect algebraically
pseudoholomorphic strips.
- DUSA MCDUFF, SUNY, Stony Brook
Toric and symplectic automorphism groups
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Every toric manifold M has a natural automorphism group A that is
a maximal compact subgroup of the symplectomorphism group S of M.
I will discuss recent work due to Susan Tolman and myself concerning
the relation between these groups. In particular I will discuss the
question of when the induced map p1 (A) ® p1 (S) is
injective. It turns out that toric manifolds for which injectivity
fails have a very special structure.
- DIETMAR SALAMON, ETH
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- CLAUDE VITERBO, Ecole Polytechnique, Palaiseau
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- JEAN-YVES WELSCHINGER, Ecole normale supérieure de Lyon, UMPA, 46, allée
d'Italie, 69364 Lyon Cedex 07
Invariants of real symplectic 4-manifolds and lower bounds in
real enumerative geometry
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I will define invariants under deformation of real symplectic
4-manifolds. These invariants are obtained via an algebraic count of
real rational J-holomorphic curves which pass through a given
configuration of points, for a generic almost complex structure J.
These invariants provide lower bounds in real enumerative geometry,
namely for the total number of such real rational J-holomorphic
curves.
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