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A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS

JIM HOSTE

Department of Mathematics, Pitzer College, Claremont, CA 91711, USA

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and

PATRICK D. SHANAHAN

Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045, USA

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https://doi.org/10.1142/S0218216504003081Cited by:50 (Source: Crossref)

Abstract

The fundamental group of a 2-bridge knot has a particularly nice presentation, having only two generators and a single relation. For certain families of 2-bridge knots, such as the torus knots, or the twist knots, the relation takes on an especially simple form. Exploiting this form, we derive a formula for the A-polynomial of twist knots. Our methods extend to at least one other infinite family of (non-torus) 2-bridge knots. Using these formulae we determine the associated Newton polygons. We further prove that the A-polynomials of twist knots are irreducible.

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