Recent results in contact form geometry. (Q1433903)

The author announces some new results in contact form geometry. These results are related to a new homology obtained by using a variational problem on Legendrian curves. This homology is generated by a part of the Morse complex of the variational problem which involves only periodic orbits. Because of the lack of compactness, it has some additional part which has been discussed in an earlier work by the author [A homology associated to a contact form on a space dual Legendrian curves, to appear]. He gives a more restrictive characterization of this additional part which should allow to compute it precisely.