Natural quotients on split supercotangent bundles and their canonical supersymplectic structures

Muñoz-Masqué, J.; Sánchez-Valenzuela, O. A.

doi:10.1016/s0926-2245(00)00006-1

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Connections On Supermanifolds2

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2014

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“…The following result, which will be essential in what follows, explains the structure of such bundles. For its proof, see [11]. Next, we define graded connections, mimicking the notion of classical Koszul connection (see [5], [7]).…”

Section: Connections On Supermanifoldsmentioning

confidence: 99%

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Quillen superconnections and connections on supermanifolds

Beltrán

Monterde

Vallejo

2014

Journal of Geometry and Physics

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Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the curvatures of both kind of connections, and their associated Chern classes, is discussed in detail. In particular, we find that Chern classes for graded vector bundles on split supermanifolds can be computed through the associated Quillen superconnections.Comment: First versio

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Section: Connections On Supermanifoldsmentioning

confidence: 99%

“…The following result, which will be essential in what follows, explains the structure of such bundles. For its proof, see [11].…”

Section: Connections On Supermanifoldsmentioning

confidence: 99%