Divisibility conjecture for Conway polynomials of links in rational homology spheres

From papers

Let KK be a null-homologous oriented kk-component link with zero pairwise linking numbers in a rational homology sphere Σ\Sigma, and let LL be an admissible link of ellell components in (Σ,K)(\Sigma,K). Divisibility conjecture. Then

z2k2+ divides K([Σ,L]).z^{2k-2+\ell}\text{ divides }\nabla_K([\Sigma,L]).

This conjecture generalizes the preceding divisibility theorem from knots to links and is intended to study Conway polynomials of manifolds with higher first Betti number. The case =0\ell=0 was recently proved by Levine, while the general case is unresolved in the supplied source.

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Sources & referencesView supporting material

Primary source

Tim D. Cochran and Paul Melvin, “Finite type invariants of 3-manifolds”, arXiv:math/9805026 (1999).

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