# Structures on M x I (Ex)

From Manifold Atlas

Let be a closed oriented topological manifold of dimension and let denote the pseudo-isotopy group of orientation preserving self homeomorphisms of : two self homeomorphisms and are pseudo-isotopic if they extend to a homeomorphism : the group operation is composition. Let

be the subgroup of equivalences classes which are homotopic to the identity.

**Exercise 0.1.**
Using the fact that the topological surgery exact sequence is a long exact sequence of *abelian* groups show that is abelian.