Friday, April 5, 2013

1304.1371 (G. Sardanashvily)

Remark on the Serre-Swan theorem for graded manifolds    [PDF]

G. Sardanashvily
Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold $X$, a graded commutative $C^\infty(X)$-algebra $\cA$ is isomorphic to the structure ring of a graded manifold with a body $X$ iff it is the exterior algebra of some projective $C^\infty(X)$-module of finite rank. In particular, it follows that odd fields in field theory on a smooth manifold $X$ can be represented by graded functions on some graded manifold with body $X$.
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