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Abstract
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By a construction of Berstein and Edmonds every proper branched cover
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
to the target manifold. For proper branched covers between
-manifolds
the monodromy space is known to be a manifold. We show that this does not generalize to
dimension
by constructing a self-map of the 3-sphere for which the monodromy space is not a
locally contractible space.
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Keywords
branched covering, monodromy space
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Mathematical Subject Classification
Primary: 57M12
Secondary: 30C65
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Milestones
Received: 2 December 2016
Revised: 29 April 2022
Accepted: 12 June 2022
Published: 28 August 2022
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