A topological version of Bertini's theorem
Volume 61 / 1995
Annales Polonici Mathematici 61 (1995), 89-93
DOI: 10.4064/ap-61-1-89-93
Abstract
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 $π_V: V → Y$ 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)\V).
