Commit 2023-02-24 15:00 5be98b95
View on Github →feat(geometry/manifold/vector_bundle): smooth_fiberwise_linear
groupoid (#17302)
Let B
be a smooth manifold and F
a normed space. We build the groupoid of local homeomorphisms of B × F
which are "smooth and fibrewise linear": that is, they are of the form λ x, (x.1, φ x.1 x.2)
for some function φ
from B
to the automorphisms of F
, which is smooth and has smooth inverse on the proposed domain.
Membership in this groupoid is the natural property characterizing the transition functions of a smooth vector bundle over B
modelled on F
.