Bitwist manifolds and two-bridge knots

James W.  Cannon; William J. Floyd; LeeR Lambert; Walter R.  Parry; Jessica S. Purcell

doi:10.2140/pjm.2016.284.1

Bitwist manifolds and two-bridge knots

James W. Cannon, William J. Floyd, LeeR Lambert, Walter R. Parry, Jessica S. Purcell

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

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 bitwisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bitwist construction is often efficient and natural. Finally, we give applications to computations of fundamental groups and homology of these branched cyclic covers.

Original language	English
Pages (from-to)	1-39
Number of pages	39
Journal	Pacific Journal of Mathematics
Volume	284
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2016.284.1
Publication status	Published - Sep 2016

Keywords

Bitwist manifolds
Branched cyclic covers
Two-bridge knots

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10.2140/pjm.2016.284.1

Cite this

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AU - Parry, Walter R.

AU - Purcell, Jessica S.

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KW - Branched cyclic covers

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DO - 10.2140/pjm.2016.284.1

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JF - Pacific Journal of Mathematics

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Bitwist manifolds and two-bridge knots

Abstract

Keywords

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Quantum invariants and hyperbolic manifolds in three-dimensional topology

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Bitwist manifolds and two-bridge knots

Abstract

Keywords

Access to Document

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Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this