Topological study of foliations and contact structures

重点研究了三维、四维和五维空间上的接触结构和接触结构。重点研究了重要实例的构造及其相互关系。研究了许多数学理论的相互作用，如与奇点有关的Milnor纤丝、流体力学、作为经典力学精化的辛几何以及反映在这些结构和对象上的几个复变量。这项研究也被理解为考察这些结构的紧密性反映在曲面的测地线流上，这就产生了一类特殊的流，称为‘Anosov流’。

Foliations and contact structures are studied, with a focus on those structures on 3, 4, and 5 dimensional spaces. Especially the construction of important examples and their mutual relationships are investigated. Interactions of many mathematical theories such as Milnor fibrations associated with singularities, fluid mechanics, symplectic geometry which is a refinement of classical mechanics, and several complex variables, re flected on those structures and objects are studied.This study is also understood as looking at the tightness of those structures which is interpreted as the result of such mathematical theories are reflected on the geodesic flows of surfaces, which gives rise to a special class of flows called `Anosov flows'.