Currently, the method total_space of a vector bundle does not contain any topological information. Moreover, the dimensions do not match:

sage: M = Manifold(3, 'M')
sage: E = M.vector_bundle(2, 'E')
sage: E.total_space()
6-dimensional differentiable manifold E

This ticket attempts to fix this.

CC: @egourgoulhon @tscrim

Component: manifolds

Keywords: vector_bundles

Issue created by migration from https://trac.sagemath.org/ticket/34173