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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The axioms of supermanifolds and a new structure arising from them

Author: Mitchell J. Rothstein
Journal: Trans. Amer. Math. Soc. 297 (1986), 159-180
MSC: Primary 58A50; Secondary 58C50
MathSciNet review: 849473
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Abstract: An analysis of supermanifolds over an arbitrary graded-commmutative algebra is given, proceeding from a set of axioms the first of which is that the derivations of the structure sheaf of a supermanifold are locally free. These axioms are satisfied not by the sheaf of ${G^\infty }$ functions, as has been asserted elsewhere, but by an extension of this sheaf. A given ${G^\infty }$ manifold may admit many supermanifold extensions, and it is unknown at present whether there are ${G^\infty }$ manifolds that admit no such extension. When the underlying graded-commutative algebra is commutative, the axioms reduce to the Berezin-Kostant supermanifold theory.

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Article copyright: © Copyright 1986 American Mathematical Society