| Título: | Gauge forms on SU(2)-bundles |
| Autores: | Castrillón López, Marco ; Muñoz Masqué, Jaime |
| Tipo de documento: | texto impreso |
| Editorial: | Elsevier, 1999-07 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/restrictedAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría diferencial , Tipo = Artículo |
| Resumen: |
Let ?:P?M be a principal SU(2)-bundle, let autP [resp. gauP?autP] be the Lie algebra [resp. the ideal] of all G-invariant [resp. G-invariant ?-vertical] vector fields in X(P), and let p:C(P)?M be the bundle of connections of P. A differential form ?r on C(P) of arbitrary degree 0?r?4n, n=dimM, is said to be autP-invariant [resp. gauP-invariant] if it is invariant under the natural representation of autP [resp. gauP] on X(C(P)). The Z-graded algebra over ??(M) of autP-invariant [resp. gauP-invariant] differential forms is denoted by IautP [resp. IgauP]. The basic results of this paper are the following: (1) The algebra of gauge invariant differential forms on p:C(P)?M is generated over the algebra of differential forms on M by a 4-form ?4, i.e., IgauP(C(P))=(p???(M))[?4], where the form ?4 is globally defined on C(P) by using the canonical su(s)-valued 1-form of the bundle T?(M)?su(2) and the determinant function det:su(2)?R; its local expression is ?4=14S123(dA1i?dxi?dA1j?dxj+2A2jA3kdxj?dxk?dA1i?dxi), (Aij,xj), 1?i?3, 1?j?n, being the coordinate system induced from (xj) and the standard basis (B1,B2,B3) of su(2) on C(P). (2) Assume M is connected. Then, IautP(C(P))=R[?4]. (3) The cohomology class of ?4 in H4(C(P);R) coincides with ?4?2p?(c2(P)), where c2(P) stands for the second Chern class of P. Remark that p:C(P)?M is an affine bundle and hence one has a natural isomorphism p?:H?(M;R)?H?(C(P);R). Another important remark is the following. If dimM?3, then every principal SU(2)-bundle ?:P?M is trivial and hence its Chern class vanishes, but the form ?4 is not zero although its pull-back along every section of C(P) does vanish |
| En línea: | https://eprints.ucm.es/id/eprint/24318/1/castrill%C3%B3n250pdf.pdf |
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