Abstract
Any non-split complex supermanifold is a deformation of a split supermanifold. These deformations are classified by group orbits in a non-abelian cohomology. For the case of a split supermanifold with no global nilpotent even vector fields, an injection of this non-abelian cohomology into an abelian cohomology is constructed. The cochains in the non-abelian complex appear as exponentials of cochains of nilpotent even derivations. Necessary conditions for a recursive construction of these cochains of derivations are analyzed up to terms of degree six. Results on classes of examples of supermanifolds of odd dimension up to 7 are deduced.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
