arXiv subjects

Martina Aaltonen

Publications and source records attributed to Martina Aaltonen.

4 recordsLinked to original sources

arXiv2016

Non-manifold monodromy spaces of branched coverings between manifolds

By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. For proper branched covers between 2-manifolds the monodromy space is known to be a manifold. We show that this does not generalize to dimension 3 by constructing a self-map of the 3-sphere for which the monodromy space is not a locally contractible space.

math.GT↗

arXiv2016

Local monodromy of branched covers and dimension of the branch set

We show that, if the local dimension of the branch set of a discrete and open mapping $f\colon M\to N$ 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 $f\colon M \to N$ of local multiplicity at most three between $n$-manifolds is either a covering or $fB_f$ has local dimension $(n-2)$.

math.GT↗

arXiv2015

Note on the canonical genus of a knot

We show that every canonical Seifert surface is (up to isotopy) given by a knot diagram in which the (open) Seifert disks are pairwise disjoint.

math.GT↗

arXiv2014

Monodromy representations of completed coverings

In this paper we consider completed coverings that are branched coverings in the sense of Fox. For completed coverings between PL manifolds we give a characterization of the existence of a monodromy representation and the existence of a locally compact monodromy representation. These results stem from a characterization for the discreteness of a completed normal covering. We also show that completed coverings admitting a monodromy representations are discrete and that the image of the branch set is closed.

math.GT↗