Vassiliev invariants for pretzel knots

Abstract

We compute Vassiliev invariants up to order six for arbitrary pretzel knots, which depend on $g+1$ parameters $n_1,\dots ,n_{g+1}$. These invariants are symmetric polynomials in $n_1,\dots ,n_{g+1}$ whose degree coincide with their order. We also discuss their topological and integer-valued properties.

14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1112.5406

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Cited by in corpus (3)

• Chern-Simons perturbative series revisited
• Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
• Algebraic structures of Vassiliev invariants for knot families