# Talk:Inertia group I (Ex)

From Manifold Atlas

Revision as of 14:56, 30 August 2013 by Marek Kaluba (Talk | contribs)

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?)*