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The study of higher tangential structures, arising from higher connectedcovers of Lie groups (String, Fivebrane, Ninebrane structures), requireconsiderable machinery for a full description, especially for connections togeometry and applications. With utility in mind, in this paper we study thesestructures at the rational level and by considering Lie groups as a startingpoint for defining each of the higher structures, making close connection to$p_i$-structures. We indicatively call these (rational) Spin-Fivebrane andSpin-Ninebrane structures. We study the space of such structures andcharacterize their variations, which reveal interesting effects wherebyvariations of higher structures are arranged to systematically involve lowerones. We also study the homotopy type of the gauge group corresponding tobundles equipped with the higher rational structures that we define.

Variations of rational higher tangential structures