The Jones polynomial and boundary slopes of alternating Montesinos knots
Taylor, Samuel J.
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We show for an alternating knot the minimal boundary slope of an essential spanning surface is given by the signature plus twice the minimum degree of the Jones polynomial and the maximal boundary slope of an essential spanning surface is given by the signature plus twice the maximum degree of the Jones polynomial. For alternating Montesinos knots, these are the minimal and maximal boundary slopes.
Curtis, C. L., & Taylor, S. J. (n.d). THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS. Journal Of Knot Theory And Its Ramifications, 20(10), 1345-1354.
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