We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).
@article{bwmeta1.element.bwnjournal-article-apmv61z1p89bwm,
author = {Artur Pi\k ekosz},
title = {A topological version of Bertini's theorem},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {89-93},
zbl = {0828.57004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p89bwm}
}
Artur Piękosz. A topological version of Bertini's theorem. Annales Polonici Mathematici, Tome 62 (1995) pp. 89-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p89bwm/
[000] [1] S. S. Abhyankar, Local Analytic Geometry, Academic Press, New York and London, 1964.
[001] [2] A. Piękosz, Basic definitions and properties of topological branched coverings, to appear. | Zbl 0891.57004