Cobordism, Relative Indices and Stein Fillings

Cusp geometry and the cobordism invariance of the index

The cobordism invariance of the index on closed manifolds is reproved using the calculus of cusp pseudodifferential operators on a manifold with boundary. More generally, on a compact manifold with corners, the existence of a symmetric cusp differential operator of order 1 and of Dirac type near the boundary implies that the sum of the indices of the induced operators on the hyperfaces is null.

非紧对称空间上的Stein-Weiss不等式

Stein-Weiss inequality on non-compact symmetric spaces

本文完整刻画了任意秩非紧对称空间上Laplace-Beltrami算子相关算子族Stein-Weiss不等式成立的充要条件，并由此得到容许指标集更大的加权泛函不等式。

Subelliptic Spin_c Dirac operators, III The Atiyah-Weinstein conjecture

In this paper we show that there is a well defined modified dbar-Neumann problem for a spin_c manifold with a strictly pseudoconvex boundary (in the contact geometry sense). We show that the index of the associated boundary value problem can be computed as the relative index between the Calderon projector on the boundary and the projector defining the boundary condition. To make sense of this statement we need to develop a considerable extension of the classical notion of a Fredholm pair of subspaces of a Hilbert space. We call this the theory of "tame Fredholm pairs;" it is presented in the a…