# Duality functors for $n$-fold vector bundles

@article{Graciasaz2012DualityFF, title={Duality functors for \$n\$-fold vector bundles}, author={Alfonso Gracia-saz and Kirill C. H. Mackenzie}, journal={arXiv: Differential Geometry}, year={2012} }

Double vector bundles may be dualized in two distinct ways and these duals are themselves dual. These two dualizations generate a group, denoted $\mathscr{D}\mathscr{F}_2$, which is the symmetric group $S_3$ on three symbols. In the case of triple vector bundles the authors proved in a previous paper that the corresponding group $\mathscr{D}\mathscr{F}_3$ is an extension of $S_4$ by the Klein four-group. In this paper we show that the group $\mathscr{D}\mathscr{F}_n$, for $n$-fold vector…

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