Variations of rational higher tangential structures

TL;DR

This paper investigates rational higher tangential structures derived from Lie groups, exploring their variations, relationships with lower structures, and the homotopy types of associated gauge groups, to facilitate geometric and application-oriented understanding.

Contribution

It introduces rational models of higher tangential structures like Spin-Fivebrane and Spin-Ninebrane, analyzing their variations and gauge group homotopy types, connecting higher and lower structures systematically.

Findings

Variations of higher structures involve lower structures systematically.

Homotopy types of gauge groups for these structures are characterized.

Rational models simplify the study of complex higher tangential structures.

Abstract

The study of higher tangential structures, arising from higher connected covers of Lie groups (String, Fivebrane, Ninebrane structures), require considerable machinery for a full description, especially for connections to geometry and applications. With utility in mind, in this paper we study these structures at the rational level and by considering Lie groups as a starting point for defining each of the higher structures, making close connection to $p_i$-structures. We indicatively call these (rational) Spin-Fivebrane and Spin-Ninebrane structures. We study the space of such structures and characterize their variations, which reveal interesting effects whereby variations of higher structures are arranged to systematically involve lower ones. We also study the homotopy type of the gauge group corresponding to bundles equipped with the higher rational structures that we define.