A fake smooth $\mathbf{CP}^2\#\mathbf{RP}^4$
Daniel Ruberman and Ronald J. Stern
We show that the manifold $*\mathbf{RP}^4 \# *\mathbf{CP}^2$, which is homotopy equivalent but not homeomorphic to $\mathbf{RP}^4 \# \mathbf{CP}^2$, is in fact smoothable.