Nonmanifold monodromy spaces of branched coverings between manifolds

Martina Aaltonen

Vol. 319 (2022), No. 1, 1–16

DOI: 10.2140/pjm.2022.319.1

Abstract

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.

Keywords

branched covering, monodromy space

Mathematical Subject Classification

Primary: 57M12

Secondary: 30C65

Milestones

Received: 2 December 2016

Revised: 29 April 2022

Accepted: 12 June 2022

Published: 28 August 2022