Tangle sums and factorization of a-polynomials

Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa

Research output: Contribution to journalArticle

Abstract

We show that there exist infinitely many examples of pairs of knots, K1 and K2, that have no epimorphism π1(S3 \ K1) → π1(S3 \ K2) preserving peripheral structure although their A-polynomials have the factorization AK2 (L, M) ∣ AK1 (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 languageEnglish
Pages (from-to)823-835
Number of pages13
JournalNew York Journal of Mathematics
Volume21
Publication statusPublished - 2015 Jan 1
Externally publishedYes

Fingerprint

Tangles
Epimorphism
Factorization
A-polynomial
Levenberg-Marquardt
Knot
Polynomial
Converse

Keywords

  • A polynomial
  • Knot group
  • Tangle sum

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Tangle sums and factorization of a-polynomials. / Ishikawa, Masaharu; Mattman, Thomas W.; Shimokawa, Koya.

In: New York Journal of Mathematics, Vol. 21, 01.01.2015, p. 823-835.

Research output: Contribution to journalArticle

Ishikawa, M, Mattman, TW & Shimokawa, K 2015, 'Tangle sums and factorization of a-polynomials', New York Journal of Mathematics, vol. 21, pp. 823-835.
Ishikawa, Masaharu ; Mattman, Thomas W. ; Shimokawa, Koya. / Tangle sums and factorization of a-polynomials. In: New York Journal of Mathematics. 2015 ; Vol. 21. pp. 823-835.
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