Projective Modules of Finite Type over the Supersphere S²,²

الأصل · EN

In the spirit of noncommutative geometry we construct all inequivalent vector bundles over the (2,2)-dimensional supersphere S²,² 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 S²,². The canonical connection ∇ = p ∘ d is used to compute the Chern numbers by means of the Berezin integral on S²,². 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 S²,².