### Abstract

In 1969, J. H. Conway gave efficient methods of calculating abelian invariants of classical knots and links. The present paper includes a detailed exposition (with new proofs) of these methods and extensions in several directions. The main application given here is as follows. A link L of two unknotted components in S3 has the distinct lifting property for p if the lifts of each component to the /7-fold cover of S3 branched along the other are distinct. The /7-fold covers of these lifts are homeomorphic, and so L gives an example of two distinct knots with the same /7-fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all p > 2.

Original language | English (US) |
---|---|

Pages (from-to) | 75-109 |

Number of pages | 35 |

Journal | Transactions of the American Mathematical Society |

Volume | 270 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1982 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*270*(1), 75-109. https://doi.org/10.1090/S0002-9947-1982-0642331-X

**A family of links and the conway calculus.** / Giller, Cole A.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 270, no. 1, pp. 75-109. https://doi.org/10.1090/S0002-9947-1982-0642331-X

}

TY - JOUR

T1 - A family of links and the conway calculus

AU - Giller, Cole A.

PY - 1982/3

Y1 - 1982/3

N2 - In 1969, J. H. Conway gave efficient methods of calculating abelian invariants of classical knots and links. The present paper includes a detailed exposition (with new proofs) of these methods and extensions in several directions. The main application given here is as follows. A link L of two unknotted components in S3 has the distinct lifting property for p if the lifts of each component to the /7-fold cover of S3 branched along the other are distinct. The /7-fold covers of these lifts are homeomorphic, and so L gives an example of two distinct knots with the same /7-fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all p > 2.

AB - In 1969, J. H. Conway gave efficient methods of calculating abelian invariants of classical knots and links. The present paper includes a detailed exposition (with new proofs) of these methods and extensions in several directions. The main application given here is as follows. A link L of two unknotted components in S3 has the distinct lifting property for p if the lifts of each component to the /7-fold cover of S3 branched along the other are distinct. The /7-fold covers of these lifts are homeomorphic, and so L gives an example of two distinct knots with the same /7-fold cover. The above machinery is then used to construct an infinite family of links, each with the distinct lifting property for all p > 2.

UR - http://www.scopus.com/inward/record.url?scp=84968468639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968468639&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1982-0642331-X

DO - 10.1090/S0002-9947-1982-0642331-X

M3 - Article

AN - SCOPUS:84968468639

VL - 270

SP - 75

EP - 109

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -