Projective Modules of Finite Type over the Supersphere $S^{2,2}$}

Details Projective Modules of Finite Type over the Supersphere $S^{2,2}$} Projective Modules of Finite Type over the Supersphere $S^{2,2}$}

1999-07-26

arxiv.org/abs/math-ph/9907020v1

Differ.Geom.Appl. 14 (2001) 95-111

Physics

Mathematical Physics

1+16 pages. latex

Scientific paper

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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