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.
|Number of pages||13|
|Journal||New York Journal of Mathematics|
|Publication status||Published - 2015 Jan 1|
- A polynomial
- Knot group
- Tangle sum
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