[Transformations logarithmiques sur la surface de Hopf]
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.
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.
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@article{CRMATH_2006__342_1_37_0,
author = {Zentner, Raphael},
title = {A note on logarithmic transformations on the {Hopf} surface},
journal = {Comptes Rendus. Math\'ematique},
pages = {37--42},
publisher = {Elsevier},
volume = {342},
number = {1},
year = {2006},
doi = {10.1016/j.crma.2005.10.030},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.10.030/}
}
TY - JOUR AU - Zentner, Raphael TI - A note on logarithmic transformations on the Hopf surface JO - Comptes Rendus. Mathématique PY - 2006 SP - 37 EP - 42 VL - 342 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.10.030/ DO - 10.1016/j.crma.2005.10.030 LA - en ID - CRMATH_2006__342_1_37_0 ER -
%0 Journal Article %A Zentner, Raphael %T A note on logarithmic transformations on the Hopf surface %J Comptes Rendus. Mathématique %D 2006 %P 37-42 %V 342 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.10.030/ %R 10.1016/j.crma.2005.10.030 %G en %F CRMATH_2006__342_1_37_0
Zentner, Raphael. A note on logarithmic transformations on the Hopf surface. Comptes Rendus. Mathématique, Tome 342 (2006) no. 1, pp. 37-42. doi : 10.1016/j.crma.2005.10.030. http://archive.numdam.org/articles/10.1016/j.crma.2005.10.030/
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