Displaying similar documents to “A new geometric invariant associated to the space of flat connections”

Equivariant cohomology of the skyrmion bundle

Gross, Christian

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The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps U : M → SU N F he thinks of the meson fields as of global sections in a bundle B ( M , SU N F , G ) = P ( M , G ) × G SU N F . For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with N F ≤ 6 , one has H * ( E G × G SU N F ) ≅ H * ( SU N F ) G ≅ S ( G ̲ * ) ⊗ H * ( SU N F ) ≅ H * ( B G ) ⊗ H * ( SU N F ) , where E G ( B G , G ) is the universal...

Natural operators in the view of Cartan geometries

Martin Panák (2003)

Archivum Mathematicum

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We prove, that r -th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order ( 1 , 0 ) (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order r - 1 . On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem...