What is Semi-s-cobordism?

In mathematics, a cobordism of an -dimensional manifold W between its boundary components, two n-manifolds M and M, is called a semi-s-cobordism if the inclusion M ↪ W {\displaystyle M\hookrightarrow W} is a simple homotopy equivalence , with no further requirement on the inclusion M − ↪ W {\displaystyle M^{-}\hookrightarrow W} .