The discussion revolves around the concept of connections on principal bundles and their relationship to connections in the context of tangent vector spaces. Participants explore the definitions and implications of these connections, considering their generality and specific applications.
Participants present differing views on the relationship between connections on principal bundles and tangent vector spaces, indicating that multiple competing perspectives exist without a consensus.
Some statements depend on specific definitions of connections and may involve assumptions that are not explicitly stated. The discussion does not resolve the complexities of these relationships.
Yes, equipped with an additional, continuous group operation which allows to jump from one point to another via elements of the group.kent davidge said:I read about connections on principal bundles. I don't have the knowledge nor the time to learn about principal bundles in the first place. Never the less this makes me wonder if such connections are the same as those talked about in the context of tangent vector spaces. Are they the same thing?