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Taylor series coefficients of the HP-polynomial as an invariant for links in the solid torus |
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PP: 203-208 |
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Author(s) |
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K. Bataineh,
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Abstract |
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| We show that the coe±cients of a reformulation of a Taylor series expansion of the Hoste and Pryzyticki
polynomial are Vassiliev invariants. We also show that many other reformulations of the Taylor series expansion have
coe±cients that are Vassiliev invariants. We charecterize the ¯rst two coe±cients b1
0(t) and bL
1 (t) for one of these expan-
sions. Moreover, the second coe±cient bL
1 (t); which is a type-one Vassiliev invariant, is given two explicit computational
formulas, which are easy to calculate. bL
1 (t) is used to give a lower bound for the crossing number of a knot of zero
winding number in the solid torus. |
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