The fourth skein module and the Montesinos-Nakanishi conjecture for 3-algebraic links

الأصل · EN

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).