A note on logarithmic transformations on the Hopf surface

In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on 4-manifolds. We will show here that this is not the case for the Hopf surface, all integer homology Hopf surfaces we obtain are diffeomorphic to the standard Hopf surface. To cite this article: R. Zentner, C. R. Acad. Sci. Paris, Ser. I 342 (2006).