Branched polynomial covering maps

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    Abstract

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved.
    Original languageEnglish
    JournalTopology and Its Applications
    Volume125
    Issue number1
    Pages (from-to)63-72
    ISSN0166-8641
    DOIs
    Publication statusPublished - 30 Oct 2002

    Keywords

    • branched polynomial covering space
    • Weierstrass polynomial
    • Riemann surface
    • knot
    • 3-manifold

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