Differential Topology
A note on logarithmic transformations on the Hopf surface
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 37-42.

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.

Dans cette note nous étudions des transformations logarithmiques au sens de la topologie différentielle le long de deux fibres de la surface de Hopf. Il est connu que ce type de transformations peut donner lieu à des structures différentiables exotiques sur les 4-variétés. Nous allons montrer que ceci n'est pas le cas pour la surface de Hopf. En effet, les surfaces de Hopf homologiques que nous obtenons sont difféomorphes à la surface de Hopf standard.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.10.030
Zentner, Raphael 1

1 Laboratoire d'analyse, de topologie, et de probabilités, université de Provence, 13013 Marseille, France
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Zentner, Raphael. A note on logarithmic transformations on the Hopf surface. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 37-42. doi : 10.1016/j.crma.2005.10.030. http://www.numdam.org/articles/10.1016/j.crma.2005.10.030/

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