Superconnections and Parallel Transport

Details Superconnections and Parallel Transport Superconnections and Parallel Transport

2007-11-18

arxiv.org/abs/0711.2766v2

Mathematics

Differential Geometry

27 pages; added references

Scientific paper

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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