The fourth skein module and the Montesinos-Nakanishi conjecture for 3-algebraic links
Abstract
We study the concept of the fourth skein module of 3-manifolds, that is a skein module based on the skein relation b0L0 + b1L1 + b2L2 + b3L3 = 0 and a framing relation L(1) = aL, where a, b0, b3 are invertible. We introdule the concept of n-algebraic tangles (and links) and analyze the skein module for 3-algebraic links. As a byproduct we prove the Montesinos-Nakanishi 3-move conjecture for 3-algebraic links (including 3-bridge links).
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