Bi-twist manifolds and two-bridge knots

We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often e...

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Bibliographic Details
Published in:arXiv.org 2015-04
Main Authors: Cannon, J W, Floyd, W J, Lambert, L, Parry, W R, Purcell, J S
Format: Article
Language:English
Subjects:
Bridge construction
Homology
Knots
Online Access:Get full text
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Summary:We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural. Finally, we give applications to computations of fundamental groups and homology of these branched cyclic covers.
ISSN:2331-8422
DOI:10.48550/arxiv.1306.4564