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A unified construction of the Alexander- and the Jones-invariant. (English) Zbl 0893.20030
Slovák, Jan (ed.), Proceedings of the 16th Winter School on geometry and physics, Srní, Czech Republic, January 13–20, 1996. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 46, 117-121 (1997).
As observed by V. F. R. Jones, the classical Burau module can be used to construct a Yang-Baxter matrix. In the paper, this approach is generalized by replacing the classical Burau module by its braid valued preimage, and the Alexander- and the Jones-invariant both are constructed from this braid module. The topological origin of the braid module is explained in terms of holonomy of flat connections and group homology.
This paper is a short overview on the works: F. Constantinescu and M. Lüdde [preprint of SFB288, Berlin, 181:5, October 1995], M. Lüdde [Math. Ann. 306, No. 3, 555-569 (1996; Zbl 0859.20030)].
For the entire collection see [Zbl 0866.00050].
20F36 Braid groups; Artin groups
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)