A relative index on the space of embeddable CR-structures, I
成果类型：
Article
署名作者：
Epstein, CL
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/120982
发表日期：
1998
页码：
1-59
关键词：
摘要：
We study the. problem of embeddability for three dimensional CR-manifolds. Let (M, (0) partial derivative(b)) denote a compact, embeddable, strictly pseudoconvex CR-manifold and S-0 the orthogonal projection on ker (0) partial derivative(b). If (1) partial derivative(b) denotes a deformation of this CR-structure then (1) partial derivative(b) is embeddable if and only if S-0: ker(1) partial derivative(b) --> ker(0) partial derivative(b) is a Fredholm operator. We define the relative index, Ind((0) partial derivative(b), (1) partial derivative(b)), to be the Fredholm index of this operator. This integer is shown to be independent of the volume form used to define S-0 and to be constant along orbits of the group of contact transformations. The relative index therefore defines a stratification of the moduli space of embeddable CR-structures. For small perturbations its value is related to small eigenvalues of the associated square(b)-operator.