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Complex supermanifolds of odd dimension beyond 5


Author: Matthias Kalus
Journal: Proc. Amer. Math. Soc. 145 (2017), 2749-2756
MSC (2010): Primary 58A50, 58H15
DOI: https://doi.org/10.1090/proc/13428
Published electronically: December 9, 2016
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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.


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Matthias Kalus
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
Email: matthias.kalus@rub.de

DOI: https://doi.org/10.1090/proc/13428
Keywords: non-abelian cohomology; complex supermanifold; deformation
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
Article copyright: © Copyright 2016 American Mathematical Society