We briefly survey the existing concepts of a supermanifold, touching upon the Berezin-Leites-Kostant approach and the DeWitt-Rogers supermanifolds. Building upon Rothstein's axiomatics, we introduce the category of R^\infty supermanifolds, and show that - when the ground algebra B satisfies a mild technical requirement - they can be defined in terms of a local model. When B=R (the real numbers), the category of R^\infty-supermanifolds reduces to the Berezin-Leites-Kostant category, while when B is a finite-dimensional exterior algebra the category og G-supermanifolds, previuously introduced by some of the present authors, is recovered.
Supermanifold theory: towards a unifying approach
BARTOCCI, CLAUDIO;
1996-01-01
Abstract
We briefly survey the existing concepts of a supermanifold, touching upon the Berezin-Leites-Kostant approach and the DeWitt-Rogers supermanifolds. Building upon Rothstein's axiomatics, we introduce the category of R^\infty supermanifolds, and show that - when the ground algebra B satisfies a mild technical requirement - they can be defined in terms of a local model. When B=R (the real numbers), the category of R^\infty-supermanifolds reduces to the Berezin-Leites-Kostant category, while when B is a finite-dimensional exterior algebra the category og G-supermanifolds, previuously introduced by some of the present authors, is recovered.
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