nLab quaternionic vector bundle

1. Idea

A vector bundle with fibers quaternionic vector spaces.

2. Related concepts

• real vector bundle, complex vector bundle

• quaternionic oriented cohomology theory

• quaternionic K-theory

3. References

General

• Semyon Alesker, A topological obstruction to existence of quaternionic Plucker map, in: Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics, vol 1850. Springer, (arXiv:math/0111028, doi:10.1007/978-3-540-44489-3_1)

Quaternionic line bundles

• Gustavo Granja, On quaternionic line bundles, MIT 1999 (dspace:1721.1/85302, pdf)

• Diarmuid Crowley, Sebastian Goette, Kreck-Stolz invariants for quaternionic line bundles, Transactions of the American Mathematical Society Vol. 365, No. 6 (2013), pp. 3193-3225 (arXiv:1012.5237, jstor:23513538)

Relation to 4-cohomotopy over 5-manifolds:

• Panagiotis Konstantis, Vector bundles and cohomotopies of spin 5-manifolds, Homology, Homotopy and Applications Volume 23 (2021) Number 1 (arXiv:1812.06547, doi:10.4310/HHA.2021.v23.n1.a9)