Edge polynomials, Newton and norm polygons of a family of hyperbolic manifolds
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We present an infinite family of knot manifolds whose edge polynomials have a root of unity of order 4. More precisely, consider the family of knot manifolds M 4 k +2 obtained by Dehn filling along one of the boundary components of the Whitehead link exterior with slope 4 k + 2, k ≥ 1 (w.r.t. the standard meridian-longitude coordinates). Then the slope 1/ k is a strongly detected boundary slope of M 4 k +2 to which a root of unity of order 4 is associated. This is the first example of such an infinite family of 3-manifolds. For this family of knot manifolds, we also completely determine their norm polygons and Newton polygons.