Résumé :

We consider the topological quantum field theory properties of sutured Floer homology, as introduced by Honda--Kazez--Matic. We present several results in the ``dimensionally reduced" case of product manifolds. The SFH of such manifolds reduces to that of solid tori, and forms a ``categorification of Pascal's triangle". Contact

structures correspond to chord diagrams, and contact elements form

distinguished subsets of SFH of order given by the Catalan numbers. We find natural ``creation and annihilation operators'' which allow us to define a QFT-type basis of SFH, consisting of contact elements. In fact sutured Floer homology in this case reduces to the combinatorics

of chord diagrams, and in a sense which can be made precise, is the

``quantum field theory of two non-commuting particles". The details of

this description have intrinsic contact-topological meaning, allowing

us for instance to compute certain contact categories, and to give a

``contact geometry free" proof that the contact element of a contact

structure with torsion is zero.