Dear all, sorry for not having posted anything so far but my master thesis (stable classification of certain families of four manifolds) and PhD interviews have been keepingÂ me very busy đ

This is a quick exercise which I was asked to solve by a friend of mine and since I found it funny I decided to spell some more details about it in order to show the importance of the Bockstein exact sequence. This could be a typical exam exercise in “Topology 2” here in Bonn, so dear fellows students, read and comment if anything is unclear!

The followingÂ is exercise 7, page 366 from **Bredon’s Topology and Geometry**:

Show that there can be no -manifold with