On the Wu classes of the topological blow up

Abstract

We mainly discuss the Wu classes $v(M)$ and the Steenrod operation $Sq$ of the topological blow up $\tilde{M}$. The formula of the Wu class $v(\tilde{M})$ will be given as well as the formula of the Steenrod operation $Sq$. As an application, we will use our results to describe a geometric obstruction.