Branched polynomial covering maps

Vagn Lundsgaard Hansen

doi:10.1016/S0166-8641(01)00259-0

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 language	English
Journal	Topology and Its Applications
Volume	125
Issue number	1
Pages (from-to)	63-72
ISSN	0166-8641
DOIs	https://doi.org/10.1016/S0166-8641(01)00259-0
Publication status	Published - 30 Oct 2002

Keywords

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

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10.1016/S0166-8641(01)00259-0

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AB - 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.

KW - branched polynomial covering space

KW - Weierstrass polynomial

KW - Riemann surface

KW - knot

KW - 3-manifold

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DO - 10.1016/S0166-8641(01)00259-0

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JO - Topology and Its Applications

JF - Topology and Its Applications

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Branched polynomial covering maps

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Keywords

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