Infinitely many knots with the same polynomial invariant
Infinitely many knots with the same polynomial invariant
We give infinitely many examples of infinitely many knots in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S cubed"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{S^3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the same recently discovered two-variable and Jones polynomials, but distinct Alexander module structures, which are hyperbolic, fibered, ribbon, of …