# Connections and Parallel Transport

@article{Dumitrescu2009ConnectionsAP, title={Connections and Parallel Transport}, author={Florin Dumitrescu}, journal={arXiv: Differential Geometry}, year={2009} }

In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.

## 5 Citations

1|1 Parallel Transport and Connections

- Mathematics
- 2010

A vector bundle with connection over a supermanifold leads naturally to a notion of parallel transport along superpaths. In this note we show that {\it every} such parallel transport along superpaths…

A new look at connections

- Mathematics
- 2011

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over…

Connections on smooth Lie algebra bundles

- Mathematics
- 2019

We define the notion of Lie Ehresmann connection on Lie algebra bundles and show that a Lie connection on a Lie algebra bundle induces a Lie Ehresmann connection. The converse is proved for normed…

Principal Bundles and Gauge Theories

- Physics, Mathematics
- 2011

This set of lecture notes fills a hole that in the authors opinion currently exists in the available literature on (prequantum or first quantised) gauge theory: theoretical physics texts do lots of…

The character map in equivariant twistorial Cohomotopy implies the Green-Schwarz mechanism with heterotic M5-branes

- Physics, Mathematics
- 2020

The celebrated Green-Schwarz mechanism in heterotic string theory has been suggested to secretly underly a higher gauge theoretic phenomenon, embodying a higher Bianchi identity for a higher-degree…

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