Vol. 319, No. 1, 2022

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Nonmanifold monodromy spaces of branched coverings between manifolds

Martina Aaltonen

Vol. 319 (2022), No. 1, 1–16

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.

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branched covering, monodromy space
Mathematical Subject Classification
Primary: 57M12
Secondary: 30C65
Received: 2 December 2016
Revised: 29 April 2022
Accepted: 12 June 2022
Published: 28 August 2022
Martina Aaltonen
University of Helsinki