A-polynomials of a family of two-bridge knots

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Abstract

The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an explicit resultant. We present this resultant in two different ways. We determine a recursive definition for the A-polynomials of the J(4, 2n) and J(5, 2n) knots, and for the canonical component of the A-polynomials of the J(2n, 2n) knots. Our work also recovers the A-polynomials of the J(1, 2n) knots, and the recursive formulas for the A-polynomials of the A(2, 2n) and A(3, 2n) knots as computed by Hoste and Shanahan.

Original languageEnglish (US)
Pages (from-to)847-881
Number of pages35
JournalNew York Journal of Mathematics
Volume21
StatePublished - Sep 8 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015, University at Albany. All rights reserved.

Keywords

  • 2-bridge knot
  • A-polynomial

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