The nonuniqueness of Chekanov polynomials of Legendrian knots
The nonuniqueness of Chekanov polynomials of Legendrian knots
Examples are given of prime Legendrian knots in the standard contact 3-space that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture of Lenny Ng.These are constructed using a new "Legendrian tangle replacement" technique.This technique is then used to show that the phenomenon of multiple Chekanov polynomials is in fact …