Sadok Kallel - The homology structure of free loop spaces

We present recent results on the structure of fibrations with section (joint with D. Sjerve), and give some applications to the theory of free loop spaces. We show how higher differentials on spherical classes in the Serre spectral sequence for the evaluation fibration associated to Map(S^k,M) are given in terms of certain homology operations in the fiber. As an illustration of our methods, we discuss the example of free loops on configuration spaces (this is a space of fundamental interest in non-linear analysis).