11:00 Marco Golla (Nantes)
Obstructing planarity of contact 3-manifolds.
Abstract: We give new obstructions to the existence of planar open books for contact structures, in terms of the homology of their fillings. I will talk about applications to links of surface singularities, Seifert fibred spaces, and integral homology spheres.
This is joint work with Paolo Ghiggini and Olga Plamenevskaya..
14:15 Jean-François Barraud (Toulouse)
A Novikov fundamental group.
Abstract: Morse theory explains how the topology of a manifold and the critical points of smooth functions on this manifold are related. The Morse homology and the associated Morse inequalities are a well known example, but there might also be deeper constraints, that are homotopic in nature and not detected by the homology.
SImilarly, the object of Novikov theory is to study how the topology of the manifold and the "critical points" of Morse closed one forms are related. Here also, there might be homotopical constraints that are not detected by the Novikov homology. I will present an agebraic invariant that captures some of this information, and is an analogue in Novikov theory of the fundamental group in Morse theory. In particular, this "Novikov fundamental group" leads to new lower bounds for the number of index 1 and 2 critical points of closed 1-forms, that are essentially different from the classical Morse-Novikov inequalities. (jw with A. Gadbled and H.V.Le).
Prochaines séances: 09/03 (A. Keating, A. Moreno, J. Solomon), 06/04 (?,?,?), 04/05 (M. Kegel, ?, ?)
Autre activité symplectique à Paris:
- Séminaire Nantes-Orsay.