Tangle sums and factorization of A-polynomials
نویسندگان
چکیده
We show that there exist infinitely many examples of pairs of knots, K1 and K2, that have no epimorphism π1(S 3 \K1)→ π1(S \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.
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