The representation-polynomial divisibility conjecture for epimorphisms of 2-bridge knot groups
Let and be canonical parabolic representations, with representation polynomials and , respectively.
Representation-polynomial divisibility conjecture. If divides , then there exists an epimorphism
The conjecture proposes that divisibility of canonical representation polynomials detects an epimorphism between the corresponding 2-bridge knot groups. The source says the converse to the known implication appears quite likely, but supplies no proof or resolution.
References
Primary source
Mikami Hirasawa and Kunio Murasugi, “Evaluations of the twisted Alexander polynomials of 2-bridge knots at 1”, arXiv:0808.3058 (2008).
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