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Recent results in contact form geometry
1.  Hill Center for the Mathematical Sciences, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 088548019, United States 
Ideally, this homology would be generated by a part of the Morse complex of the variational problem which would involve only periodic orbits. Because of the lack of compactness, it has some additional part which we had characterized in an earlier work [5].
Taking a variant of this approach, we give here a much more restrictive characterization of this additional part which should allow to compute it precisely.
This should indicate that the lack of compactness, seen as creation of additional punctures in the pseudoholomorphic approach, is much more limited than what would be theoretically allowed and leaves hope that it can be completely computed. The proof of all our claims will be published in [6].
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