| Résume | Daniel Mathews (Nantes)Sutured Floer homology and contact-topological quantum field theoryWe consider the topological quantum field theory properties of suturedFloer homology, as introduced by Honda--Kazez--Matic. We presentseveral results in the ``dimensionally reduced" case of productmanifolds. The SFH of such manifolds reduces to that of solid tori,and forms a ``categorification of Pascal's triangle". Contactstructures correspond to chord diagrams, and contact elements formdistinguished subsets of SFH of order given by the Catalan numbers. Wefind natural ``creation and annihilation operators'' which allow us todefine a QFT-type basis of SFH, consisting of contact elements. Infact sutured Floer homology in this case reduces to the combinatoricsof chord diagrams, and in a sense which can be made precise, is the``quantum field theory of two non-commuting particles". The details ofthis description have intrinsic contact-topological meaning, allowingus for instance to compute certain contact categories, and to give a``contact geometry free" proof that the contact element of a contactstructure with torsion is zero. |
