Complex supermanifolds of odd dimension beyond 5
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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 beyond 5 are deduced.References
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Additional Information
- Matthias Kalus
- Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
- MR Author ID: 930438
- Email: matthias.kalus@rub.de
- Received by editor(s): January 29, 2016
- Received by editor(s) in revised form: July 22, 2016
- Published electronically: December 9, 2016
- Communicated by: Franc Forstneric
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2749-2756
- MSC (2010): Primary 58A50, 58H15
- DOI: https://doi.org/10.1090/proc/13428
- MathSciNet review: 3626526