✦ LIBER ✦
A relative index on the space of 3-dimensional embeddable CR-structures of finite type
✍ Scribed by Peter Greiner; Wolfgang Staubach; Wei Wang
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 304 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
For a small deformation Φ of a 3‐dimensional pseudoconvex embeddable CR‐structure of finite type, we prove that Φ defines an embeddable CR‐structure if and only if the Szegö projection from ker $ ^{\rm \Phi} {\bar \partial} _{b} $ to ker $ {\bar \partial} _{b} $ is a Fredholm operator. This defines a relative index which is in this case equal to the negative of number of small eigenvalues of the operator $ ^{\rm \Phi} \bar \partial _{b}^{*} , ^{\rm \Phi} \bar \partial _{b}^{} $. We also prove a cocycle formula for the relative index. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)