# Download Contact and Symplectic Topology by Frédéric Bourgeois, Vincent Colin, András Stipsicz PDF

By Frédéric Bourgeois, Vincent Colin, András Stipsicz

Symplectic and make contact with geometry certainly emerged from the

mathematical description of classical physics. the invention of new

rigidity phenomena and houses chuffed by means of those geometric

structures introduced a brand new study box world wide. The intense

activity of many ecu learn teams during this box is reflected

by the ESF study Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the summer time university in Nantes (June 2011) and of the forged summer season institution in Budapest (July 2012) offer a pleasant landscape of many elements of the current prestige of touch and symplectic topology. The notes of the minicourses supply a gradual creation to themes that have constructed in an awesome velocity within the fresh earlier. those subject matters comprise three-dimensional and better dimensional touch topology, Fukaya different types, asymptotically holomorphic equipment in touch topology, bordered Floer homology, embedded touch homology, and adaptability effects for Stein manifolds.

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**Example text**

42 P. Massot Fig. 11. 1. Characteristic Foliations of Surfaces After the local theory which explains what happens in neighborhoods of points in contact manifolds, we want to start the semi-local theory which deals with neighborhoods of surfaces. The main tool will be characteristic foliations. The basic idea is to look at the singular foliation given on a surface S by the line ﬁeld T S ∩ ξ, see Figure 11. In order to deﬁne precisely what is a line ﬁeld with singularities, we see them as vector ﬁelds whose scale has been forgotten.

4. Convex Surfaces The goal of this section is to explain the following crucial observation by Emmanuel Giroux in 1991: If S is a generic surface in a contact 3-manifold, all the information about the contact structure near S is contained in an isotopy class of curves on S. All this section except the last subsection comes from Giroux’s PhD thesis [8], see also the webpage of Daniel Mathews for his translation of that paper into English. 42 P. Massot Fig. 11. 1. Characteristic Foliations of Surfaces After the local theory which explains what happens in neighborhoods of points in contact manifolds, we want to start the semi-local theory which deals with neighborhoods of surfaces.

17. e. a collection of disjoint simple closed curves in S. Such collections will be referred to as multi-curves. The condition −du(Y ) > 0 also implies that Γ is transverse to ξS. More precisely, Y goes from S+ = {u > 0} to S− = {u < 0} along Γ and the picture near Γ is always as in Figure 17. In the following discussion we will use several time the fact that this picture is very simple and controlled to be less precise about what happens near Γ . The last remarkable property of the decomposition of S in S+ and S− is Y expands some area form in S+ and contracts it in S− .