Study on contac structures and foliations on 3 and 4 dimensional manifolds

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Based on the notion of asymptotic linking, the head investigator proposed the framework where the study on contact structures and that on foliations would be unified, and began the research. Op the side of foliations, it turned out that exotic classes and the 1st foliated cohomology are strongly related to this framework. On the other side, the torsion invariant of contact structures has a deep relation with it. For algebraic Anosov foliations, we also established the computation of its 1st foliated cohomology and found its relation to local orbit rigidity.A research group including Miyoshi and Mitsumatsu investigated Thurston's inequality for foliations on the boundary of compact Stein surfaces and established the absolute version of the inequality for certain cases. The relative ersion and more general case are left for the future as important subject. Tsuboi and Mitsumatsu worked on the perfectness of groups of diffeomorphisms preservein certain geometric structures. Especially Tsuboi provednthe perfectness for contact diffeomorphisms and analytic diffeomorphisms of certain manifolds. Tsuboi also classified regular bi-contact structures on Seifert fibered spaces.Another group including Ono and Ohta, mainly working on contact/symlectic topology, characterized the symplectic diffeo-types of the filling of the link of simple and hyper-elliptic singularities. Also they got started the construction of obstruction theory for Lagrangian Floer homology theory.