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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The axioms of supermanifolds and a new structure arising from them
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by Mitchell J. Rothstein PDF
Trans. Amer. Math. Soc. 297 (1986), 159-180 Request permission

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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 297 (1986), 159-180
  • MSC: Primary 58A50; Secondary 58C50
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0849473-8
  • MathSciNet review: 849473