 99323 Giovanni Landi
 Projective Modules of Finite Type over the Supersphere $S^{2,2}
(51K, latex 2e)
Sep 3, 99

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Abstract. In the spirit of noncommutative geometry we construct all inequivalent
vector bundles over the $(2,2)$dimensional supersphere $S^{2,2}$ by
means of global projectors $p$ via equivariant maps. Each projector
determines the projective module of finite type of sections of the
corresponding `rank $1$' supervector bundle over $S^{2,2}$.
The canonical connection $\nabla = p \circ d$ is used to compute the
Chern numbers by means of the Berezin integral on $S^{2,2}$.
The associated connection $1$forms are graded extensions of monopoles
with not trivial topological charge.
Supertransposed projectors gives opposite values for the charges.
We also comment on the $K$theory of $S^{2,2}$.
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