Projective modules of finite type and monopoles over S2

✍ Scribed by Giovanni Landi

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 109 KB
• Volume: 37
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00032-2

✦ Synopsis

We present a unifying description of all inequivalent vector bundles over the two-dimensional sphere S 2 by constructing suitable global projectors p via equivariant maps. Each projector determines the projective module of finite type of sections of the corresponding complex rank 1 vector bundle over S 2 . The canonical connection ∇ = p • d is used to compute the topological charges. Transposed projectors give opposite values for the charges, thus showing that transposition of projectors, although an isomorphism in K-theory, is not the identity map. Also, we construct the partial isometry yielding the equivalence between the tangent projector (which is trivial in K-theory) and the real form of the charge 2 projector.