Homotopy spheres IV (Ex)

Let $M$$<wikitex>; Let $M$ be a closed smooth j$-manifold of signature zero and let $\Sigma \in bP_{4k-1}$, $k \geq 2$. {{beginthm|Exercise}} Show that there is a diffeomorphism $M \times \Sigma \cong M \times S^{4k-1}$. {{endthm}} </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]M$ be a closed smooth $4j$$4j$-manifold of signature zero and let $\Sigma \in bP_{4k-1}$$\Sigma \in bP_{4k-1}$, $k \geq 2$$k \geq 2$.

Exercise 0.1. Show that there is a diffeomorphism $M \times \Sigma \cong M \times S^{4k-1}$$M \times \Sigma \cong M \times S^{4k-1}$.