Alexander polynomial, Dijkgraaf-Witten invariant, and Seifert fibred surgery

Abstract

We apply Dijkgraaf-Witten invariant over an semiproduct of abelian groups to show that, if the $k/\ell$-surgery along a knot $K$ results in a small Seifert 3-manifold with multiplicities $a_1,a_2,a_3$, then many constraints on $k,a_1,a_2,a_3$ can be read off from the Alexander polynomial of $K$.

16 pages, 1 figure, accepted by Topology and its Applications

References in corpus (3)

• Profinite detection of 3-manifold decompositions
• The profinite completions of knot groups determine the Alexander polynomials
• Computing twisted Alexander polynomials for Montesinos links