Knot polynomials

[摘要] One of the most important invariants of the Knot type, is the one called Knot polynomials. The Knot polynomials are somehow easy to calculate, or at least they are easier to handle than other invariants of the Knot type, such as the presentation of the group of the Knot, or the elementary ideals. The Knot polynomials have important properties, that are very useful in the process of recognizing if a given polynomial can or cannot be a Knot polynomial. In this paper, we have proved that the central coefficient of the Knot polynomials cannot be zero, so the Knot polynomials always have an odd number of terms different from zero. We showed also that this central coefficient is an odd number. This coefficient is an invariant of the Knot type, and it is weaker than the Knot polynomial itself.

[发布机构] Rice University