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arXiv · 0711.2766

Superconnections and Parallel Transport

Florin Dumitrescu
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Abstract

This note addresses the construction of a notion of parallel transport along superpaths arising from the concept of a superconnection on a vector bundle over a manifold $M$. A superpath in $M$ is, loosely speaking, a path in $M$ together with an odd vector field in $M$ along the path. We also develop a notion of parallel transport associated with a connection (a.k.a. covariant derivative) on a vector bundle over a \emph{supermanifold} which is a direct generalization of the classical notion of parallel transport for connections over manifolds.

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Florin Dumitrescu. 2007-11-21. Superconnections and Parallel Transport. https://arxiv.org/abs/0711.2766

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