99-323 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 $S^{2,2}$.

Files: 99-323.src( 99-323.keywords , supermonos.tex )