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15 June 2002 Geometric branched covers between generalized manifolds
Juha Heinonen, Seppo Rickman
Duke Math. J. 113(3): 465-529 (15 June 2002). DOI: 10.1215/S0012-7094-02-11333-7

Abstract

We develop a theory of geometrically controlled branched covering maps between metric spaces that are generalized cohomology manifolds. Our notion extends that of maps of bounded length distortion, or BLD-maps, from Euclidean spaces. We give a construction that generalizes an extension theorem for branched covers by I. Berstein and A. Edmonds. We apply the theory and the construction to show that certain reasonable metric spaces that were shown by S. Semmes not to admit bi-Lipschitz parametrizations by a Euclidean space nevertheless admit BLD-maps into Euclidean space of same dimension.

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Juha Heinonen. Seppo Rickman. "Geometric branched covers between generalized manifolds." Duke Math. J. 113 (3) 465 - 529, 15 June 2002. https://doi.org/10.1215/S0012-7094-02-11333-7

Information

Published: 15 June 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1017.30023
MathSciNet: MR1909607
Digital Object Identifier: 10.1215/S0012-7094-02-11333-7

Subjects:
Primary: 57M12
Secondary: 30C65, 57P99

Rights: Copyright © 2002 Duke University Press

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Vol.113 • No. 3 • 15 June 2002
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