TSUBOI Takashi

坪井 俊つぼい たかし
TSUBOI Takashi

TSUBOI Takashi
Title Professor
Affiliation Department of Mathematics (UG), Graduate School of Mathematical Sciences
Room 415, Graduate School of Mathematical Sciences Bldg.Komaba Campus
TEL +81-3-5465-7035 | 47035(ext.)

Research Field

Topology, Dynamical Systems

Research Subject

Dynamical study of the behavior of leaves of foliations, quantitative study of foliations such as their characteristic classes, the relationship between dynamics and characteristic classes, dynamical study of infinite group actions, classifying spaces for diffeomorphism groups and the invariants of transformation groups.

Current Research

1) For infinite groups such as the group of diffeomorphisms of a compact manifold, I study their invariants for example their cohomology. It is interesting to understand the geometric meaning of the invariants. Recently I am interested in the group of volume preserving diffeomorphisms, that of symplectomorphisms, and that of contactomorphisms. The group of piecewise affine homeomorphisms and the group of real-analytic diffeomorphisms are also of interest.

(2) I also study the topology of the classifying space for foliations. It is closely related to that of the classifying space for the group of diffeomorphisms. I investigate the relationship between the invariants for foliations and the invariants for the group of diffeomorphisms.

(3) I study the contact structures of 3-dimensional manifolds, the symplectic structures of 4-dimensional maniflds, several dynamical systems on 3- or 4-dimensional manifolds,several geometric structures on them, the multi-foliations of them, etc., as well as the relationship between these structures.

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Dynamical systems. Foliations. Diffeomorphism groups. Transformation groups.Infinite group actions. Classifying spaces. Characteristic classes.