Tangle sums and factorization of A-polynomials

Details Tangle sums and factorization of A-polynomials Tangle sums and factorization of A-polynomials

2011-07-13

arxiv.org/abs/1107.2640v1

Mathematics

Geometric Topology

11 pages, 4 figures

Scientific paper

We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\pi_1(S^3\setminus K_1) \to \pi_1(S^3\setminus K_2)$ preserving peripheral structure although their A-polynomials have the factorization $A_{K_2}(L,M) \mid A_{K_1}(L,M)$. 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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