Existence of the Ehresmann connection on a manifold foliated by the locally free action of a commutative Lie group

Index theory and non-commutative geometry on foliated manifolds

This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.

切触范畴中的Ehresmann联络

Ehresmann connections in tangent categories

将Ehresmann联络推广到切触范畴，给出等价刻画并证明其推广Koszul联络，定义平行移动和曲率，证明结构方程和Bianchi恒等式。

A higher index theorem for foliated manifolds with boundary

Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For this purpose we use the Bismut local index formula in the context of non commutative geometry. This paper uses heavily the methods and technical results developed by E.Leichtnam and P.Piazza.