Talk:Inertia group I (Ex)
From Manifold Atlas
First observe, that instead of forming a connected sum we may think of it as cutting a disc
and glueing the disc back identifying boundary spheres via diffeomorphism
. By the theorem of Cerf definition of
does not depend on the embedding
.
If and
is a diffeomorphism, find a decomposition
and set
.
Conversely suppose that there exist a diffeomorphism such that
. Then glue a disc via identity to the source and target
and extend
as identity. Composition of inclusion and
,
is equal to
, hence (by definition) the target is equal to
. This proves that
.
(Is the Cerfs thm properly applied?)