On Vassiliev invariants of order two for string links

Details On Vassiliev invariants of order two for string links On Vassiliev invariants of order two for string links

2004-02-04

arxiv.org/abs/math/0402036v2

J. Knot Theory Ram. Vol. 14, No. 5 (2005), 665-687.

Mathematics

Geometric Topology

18 pages. Typos and mistakes corrected. To appear in J. Knot Th. Ramifications

Scientific paper

We show that the Casson knot invariant, linking number and Milnor's triple
linking number, together with a certain 2-string link invariant $V_2$, are
necessary and sufficient to express any string link Vassiliev invariant of
order two. Explicit combinatorial formulas are given for these invariants. This
result is applied to the theory of claspers for string links.

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