Estimation of stick index for a class of alternating links
The isotopy classification and related properties of knots and links are important research content in the field of three-dimensional manifold field.Various algebraic and geometric invariants of knots and links are practical tools for the isotopy classification of knots and links,mainly including Jones polynomials,Alexander polynomials,crossing index,stick index and so on.The stick index of knots and links is an invariant used to study the isotopy classification of knots and links from the per-spective of the combinatorial topology of three-dimensional manifold.Tangle decomposition of knots and links is a significant method for studying the isotopy classification of knots and links.It starts with the tangle decomposition of non-algebraic projections corresponding to a class of alternating links.Integer tangles at different positions are adopted by different piecewise linear construction models.The stick index estimation of the corresponding alternating links is obtained by adjusting the angle of exit edges for the existing polygonal representations of integer tangles and reducing the num-ber of edges to construct polygonal representations of tangles.
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