Signature of a finite covering space Suppose $\tilde{M}\rightarrow M$ is a finite (k-fold) covering of the smooth, oriented, compact 4-manifold $M$. Is there a relation between the signatures (http://en.wikipedia.org/wiki/Signature_(topology)) of $M$ and $\tilde{M}$?
I have a line of reasoning involving the Hirzebruch signature theorem that suggests $\sigma(\tilde{M})=k\cdot\sigma(M)$. If this is true, I would love to see independent lines of reasoning that support it.

Pontryagin numbers are multiplicative under coverings, hence, the same applies to the signature. 
