Session S39 - Differential Equations and Geometric Structures

Wednesday, July 14, 14:00 ~ 14:50 UTC-3

Group bundles and group connections

David Blázquez-Sanz

Universidad Nacional de Colombia - Sede Medellín, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

This talk is devoted to our recent findings [1, 2] about differential equations that are compatible with the group operation in a Lie group, or a Lie group bundle. Such equations are group connections. We characterize the space of group connections on a group bundle as an affine space modeled over the vector space of 1-forms with values cocycles in the Lie algebra bundle of the aforementioned group bundle. We show that group connections satisfy the Ambrose-Singer theorem and that group bundles can be seen as a particular case of associated bundles realizing group connections as associated connections. We give a construction of the Moduli space of group connections with fixed base and fiber, as an space of representations of the fundamental group of the base.

[1] B.-S, Marín, Suarez. Group bundles and group connections. arXiv:2104.04804

[2] B.-S., Marín, Ruíz. A simplified categorical approach to several Galois theories. Cahiers de topologie et géométrie différentielle catégoriques. Vol. LXI (2020) 4, 450-473.

View abstract PDF