### Abstract

We show that there exist infinitely many examples of pairs of knots, K_{1} and K_{2}, that have no epimorphism π_{1}(S^{3} \ K_{1}) → π_{1}(S^{3} \ K_{2}) preserving peripheral structure although their A-polynomials have the factorization A_{K2} (L, M) ∣ A_{K1} (L, M). Our construction accounts for most of the known factorizations of this form for knots with 10 or fewer crossings. In particular, we conclude that while an epimorphism will lead to a factorization of A-polynomials, the converse generally fails.

Original language | English |
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Pages (from-to) | 823-835 |

Number of pages | 13 |

Journal | New York Journal of Mathematics |

Volume | 21 |

Publication status | Published - 2015 Jan 1 |

Externally published | Yes |

### Keywords

- A polynomial
- Knot group
- Tangle sum

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Tangle sums and factorization of a-polynomials'. Together they form a unique fingerprint.

## Cite this

Ishikawa, M., Mattman, T. W., & Shimokawa, K. (2015). Tangle sums and factorization of a-polynomials.

*New York Journal of Mathematics*,*21*, 823-835.