## Tokyo Journal of Mathematics

### On Vassiliev Invariants of Degrees 2 and 3 for Torus Knots

Sukuse ABE

#### Abstract

We consider the $\mathbf{R}$-valued Vassiliev invariants of degrees 2 and 3 normalized by the conditions that they take values 0 on the unknot and 1 on the trefoil. We give certain answers for a problem due to N. Okuda about these two invariants. Moreover, we prove a conjecture due to Simon Willerton concerning the degree-3 Vassiliev invariant in the case of torus knots.

#### Article information

Source
Tokyo J. Math., Volume 38, Number 2 (2015), 331-337.

Dates
First available in Project Euclid: 14 January 2016

https://projecteuclid.org/euclid.tjm/1452806043

Digital Object Identifier
doi:10.3836/tjm/1452806043

Mathematical Reviews number (MathSciNet)
MR3448860

Zentralblatt MATH identifier
1337.57034

#### Citation

ABE, Sukuse. On Vassiliev Invariants of Degrees 2 and 3 for Torus Knots. Tokyo J. Math. 38 (2015), no. 2, 331--337. doi:10.3836/tjm/1452806043. https://projecteuclid.org/euclid.tjm/1452806043

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