Bitjong Ndombol Enseignant-Chercheur de [l'Université de Yaoundé 1](http://www.utdallas.edu/~ett032000/yaounde.html), sera l'invité de [Mr Jean-Claude Thomas](http://www.univ-angers.fr/Enseignant.asp?ID=1430&PAGE_RECHERCHE=1&DIS_L…) Professeur émérite du laboratoire LAREMA de Mathématiques à Angers, du 1er au 19 novembre 2009.
The closed geodesic problem has been solved by many authors under additional hypothesis. In a paper, accepted to publication in the JPAA ,
we have developed a new way to solve this problem, by defining finitely many obstructions classes. This permits to enlarge significantly the family of manifolds for which this problem is solved. Our method which relies on the concept of $A_\infty$-section of an homomorphism of differential graded algebras, shows explicitly how the natural structure of shc-algebra on the singular cochains of a space comes
into play. We expect to expand this last point during the next stay inAngers of Bitjong Ndombol.