Displaying similar documents to “No slices on the space of generalized connections.”

The associated map of the nonabelian Gauss-Manin connection

Ting Chen (2012)

Open Mathematics

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The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.

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...

Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space

Indranil Biswas (1997)

Annales de l'institut Fourier

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The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.

Connections from trivializations

Jan Kurek, Włodzimierz Mikulski (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let P be a principal fiber bundle with the basis M and with the structural group G. A trivialization of P is a section of P. It is proved that there exists only one gauge natural operator transforming trivializations of P into principal connections in P. All gauge natural operators transforming trivializations of P and torsion free classical linear connections on M into classical linear connections on P are completely described.