theta-curve polynomials and finite-type invariants

Abstract

The normalized Yamada polynomial, (R) over tilde (A), is a polynomial invariant in variable A for theta-curves. In this work, we show that the coefficients of (R) over tilde (x)(e) which is obtained by replacing A with e(x) = Sigma x(n)/n! are finite-type invariants for theta-curves although the coefficients of original (R) over tilde (A) are not finite-type. A similar result can be obtained in the case of Yokota polynomial for theta-curves.