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

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

2000-10-28

arxiv.org/abs/math/0010282v1

Mathematics

Geometric Topology

26 pages, 20 figures

Scientific paper

We study the concept of the fourth skein module of 3-manifolds, that is a skein module based on the skein relation b_0L_0 + b_1L_1 + b_2L_2 + b_3L_3 = 0 and a framing relation L^{(1)} = aL, where a, b_0, b_3 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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