Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 487-496

LOCAL MONODROMY OF BRANCHED COVERS AND DIMENSION OF THE BRANCH SET

Martina Aaltonen and Pekka Pankka

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; martina.aaltonen 'at' helsinki.fi

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; pekka.pankka 'at' helsinki.fi

Abstract. We show that, if the local dimension of the image of the branch set of a discrete and open mapping f : M → N between n-manifolds is less than (n – 2) at a point y of the image of the branch set fB_f, then the local monodromy of f at y is perfect. In particular, for generalized branched covers between n-manifolds the dimension of fB_f is exactly (n – 2) at the points of abelian local monodromy. As an application, we show that a generalized branched covering f : M → N of local multiplicity at most three between n-manifolds is either a covering or fB_f has local dimension (n – 2).

2010 Mathematics Subject Classification: Primary 57M12; Secondary 57M30, 30C65.

Key words: Branched cover, monodromy, branch set.

Reference to this article: M. Aaltonen and P. Pankka: Local monodromy of branched covers and dimension of the branch set. Ann. Acad. Sci. Fenn. Math. 42 (2017), 487-496.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4231