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Infinitely many knots with the same polynomial invariant

1986
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Proceedings of the American Mathematical Society
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We give infinitely many examples of infinitely many knots in S3 with the same recently discovered two-variable and Iones polynomials, but distinct Alexander module structures, which are hyperbolic, fibered, ribbon, of genus 2, and 3-bridge. Two knots Kx and K2 in S3 belong to the same isotopy type if there exists an orientation preserving homeomorphism of S3 which maps Kx onto K2. We denote it by Kx ~ K2. In 1984, V. Jones [9] discovered a very powerful polynomial invariant of the isotopy type

doi:10.1090/s0002-9939-1986-0831406-7
fatcat:egpjolzeu5hzfjlljnxvmw4yjq