Tangential homotopy equivalences (Ex)
From Manifold Atlas
A homotopy equivalence of closed smooth -manifolds is called stably tangential if ; i.e. pulls back the stable tangent bundle of to .
- Give an example of a stably tangential homotopy equivalence which is not homotopic to a diffeomorphism.
- Show that if is a stably tangential homotopy equivelance, then there is a diffeomorphism
such that is homotopic to , where is the projection.